Both are examples of genetic drift in which there is a change in the allele frequency when the population size becomes small. What is the difference between the two?
Genetic drift is an EVOLUTIONARY PROCESS
Source: Wikipedia > Genetic Drift
Genetic drift (also known as allelic drift or the Sewall Wright effect2 after biologist Sewall Wright) is the change in the frequency of a gene variant (allele) in a population due to random sampling of organisms.
I think that these terms are used without a perfect semantic. An obvious case
A population bottleneck is a DEMOGRAPHIC EVENT
A population bottleneck [..] is a sharp reduction in the size of a population due to environmental events (such as earthquakes, floods, fires, disease, or droughts) or human activities (such as genocide)
A founder effect is an EVOLUTIONARY PROCESS THAT RESULTS FROM A FOUNDING EVENT
Source: Provine 2004
The “founder” principle, as introduced by Mayr in 1942, was an auxiliary mechanism (less important than random drift) for producing reduced variability in an isolated population started by a few individuals or even by a single fertilized female. Mayr saw a distinction between the “founder” effect and random drift. The founders were not a random sampling of the main population, but, once isolated as a small population, would undergo random drift
In other words, a founder effect does NOT refer to the ppulation bottleneck causing by a founding event. A founder effect refers to the increase in genetic drift (loss of genetic diversity is expected) caused by a founding event. A founding event is the event by which few individuals (eventually only one) quit a large population to settle down a new small populations. As such, a founder event is a type of population bottleneck. I think that one could further extrapolate the term "founder effect" to any increase in genetic drift caused by a population bottleneck.
Do all authors use the same definitions?
I have not done a good literature review to answer this question but I would not be surprised if different authors, use slightly different definitions.
For example, some authors (e.g. Peery at al 2012, Raymond and O'Brien 1993, Duarte et al. 1992) have used the term "genetic bottleneck" instead of "population bottleneck". Wikipedia indicates that these two terms are synonyms. However I could not find any paper that formally define the term genetic bottleneck but all the papers using this term seem to be specifically interested into the genetic signature of population bottleneck. As such, the semantic relationship between population bottleneck and genetic bottleneck could be the same as between founding event and founder effect. Genetic bottleneck could be defined as the increase of genetic drift that is caused by population bottleneck.
Founder effect and population bottleneck are not necessarily examples of genetic drift. The common thing in all three is a resulting reduction in genetic diversity.
Genetic drift is a change in allele frequencies due to process of random sampling to form a finite offspring population from parent population. Ultimately some alleles gets fixed and genetic diversity decreases. However decreasing population size or small population size is not a necessity for drift to happen.
Population bottleneck and founder effect are similar population genetic events that are happening in different ecological context. Both results in decreased population size (for the population of interest) and decreased genetic diversity. But the exact ecological context determines how much of the decrease in diversity is due to drift and how much of that is due to selection.
Population bottleneck refers to an event, where a population is intact but only small portion of the individuals are able to pass their alleles to future generations. This may be associated with strong natural selection, if possessors of a trait are more fit under the condition that causes the bottleneck (if the condition is a draught, better water preserving traits would be favoured for example). Or the process may be associated with drift if individuals don't have traits that would provide them an advantage (if the condition is a volcano eruption, survivors would be random with respect to their alleles).
Founder effect refers to an event when a small subpopulation migrates to an isolated region. Isolation may be due to distance or some geographic agent. Here, again the individuals to form the subpopulation may be random with respect to their alleles, or there may be a selection towards traits that provide some advantage in migration for example.
I think that a population bottleneck is more likely to be associated with strong negative selection and a founder effect is more likely to be associated with genetic drift.
However these concepts are not about relative importance of drift and selection. (I emphasized my answer on drift/selection because the question considers them as examples of drift.) These both concepts are about the loss of genetic diversity due to decreased population size, and for that matter, I would say they are the same thing in different ecological context.
You can refer population genetics text books by Hamilton (Hamilton, 2009) or Gillespie (Gillespie, 2004) for example. You can find related discussion on sections about effective population size. There you can see that neither population (or genetic) bottleneck nor founder effect are treated as “examples” of genetic drift or defined as events caused by genetic drift.
Let me explicitly state my point. Population (or genetic) bottleneck and founder effect are events (driven by some ecological factor) of sharp but temporarily decrease in population size. Due to this decrease, genetic diversity is decreased and stays low even after population size increase again. This is an example of the case, where effective population size and census population size are very different.
Now comes the part creating the confusion: Both of these effects enhance genetic drift. But they are not caused by genetic drift. Genetic drift can be effective also when population size does not decrease.
Also they are not necessarily examples of genetic drift, meaning that, there may cases where the ecological factor causing the mentioned effects does not affect individuals within population randomly with respect to some of their traits. In that case some loci will lose its allelic diversity due to selection. But here again it is not selection that causes the mentioned effect, the cause is some ecological factor. The ecological factor causing the bottleneck may or may not cause selection. Population expansion/shrinkage is a dimension, selection/drift is another dimension.
Gillespie, J. H. (2004). Population Genetics: A Concise Guide (2nd ed.). Johns Hopkins University Press.
Hamilton, M. (2009). Population Genetics (1st ed.). Wiley-Blackwell.
The Founder and Bottleneck effect are both examples of Genetic drift as you mention. The end result is pretty much the same, i.e., a reduction in the genetic diversity of the population. The main difference is the cause underlying the drift.
Say there's a very colorful ethnically rich and all population. As in, having whites, blacks, Chinese, Indians and all.. Suddenly two blacks are for some reason disappointed and migrate to an uninhabited island. The future generations would definitely be black. So the initial population which had all these Indians Chinese and all was definitely genetically more diverse than this population of only blacks. So this Founder effect lead to a reduction in genetic diversity (compared to the original population) - due to the fact that only the blacks chose to colonise.
On the other hand, the Bottleneck effect happens when there's a natural calamity. Say, there's an earthquake in the area where our rainbow population resides. All houses have collapsed and people have died except for the house in which the blacks lived. This happened just as a matter of chance. This is very important since it should be differentiated from natural selection. If the blacks survived because they were too smart to run out of the house during the quake unlike the others or if they were too strong to hold the roof even as it was collapsing, a component of selection would be introduced since they (or their progeny) would be genetically predisposed to do a similar thing if the earth shakes sometime later.
But here in genetic drift which is another explanation for evolution, different from natural selection, its just a matter of chance.
So all in all, Founder and Bottleneck effects are different in their cause not the effect which happens to be the same.
There are some real examples which I would urge you to refer online.
Here's a reference similar, simple and crisp