From what I've read it seems that the only actual difference is that creationists use adaptation and people who believe in evolution use natural selection. But otherwise, from my understanding, the two terms are synonymous. Is that correct?
2$\begingroup$ No offense but I would love to down vote @InstructedA 's comment. (A) There are plenty of religious believes but (1) it is not our job on a science website to make a review of such beliefs and (2) your view of creationist believes is unclear and IMO wrong in the same time. (B) While believing in god (theist) or not (atheist) is correlated in accepting the theory of evolution, one can accept the theory of evolution and be theist or refuse to accept the theory of evolution and be atheist as one domain is about science while the other depends on an ideology. $\endgroup$– Remi.bJun 4, 2016 at 3:33
$\begingroup$ Always for @InstructedA (C) It is very obvious from your comment that your understanding of evolutionary processes is very limited. (D) Point "B" above is a discussion of philosophy and not biology. Point "A" above is a matter of religious studies and not biology. These topics are interesting, please open a post at the convenient location to discuss such topics. $\endgroup$– Remi.bJun 4, 2016 at 3:34
$\begingroup$ I've been teaching evolutionary biology for more than 20 years, and I don't believe in evolution (and I never will). As Tertulian once said, one believes in absurd things. Science is a matter or knowledge, not believing. $\endgroup$– user24284Jun 4, 2016 at 4:29
$\begingroup$ The down vote is not a punishment but a help for other's to recognize good from bad info. Scientists don't believe in "absolute facts" whatever that means. Natural science does not "prove facts" anyway but only offer series of evidences congruent with a hypothesis. Anyway, this is not a place to discuss that. You might want to have a watch a short introduction to philosophy of knowledge and philosophy of science. I am not going to answer further comment in this inappropriate place. $\endgroup$– Remi.bJun 4, 2016 at 15:24
$\begingroup$ I am glad that it is not a punishment, as I see and recognize massive amount of inconsistencies in the theory of evolution the way it is being presented. When I was young I was like you, but then the 'church' presented me with a much better theory. Things are so consistent. I have always hoped that the 'scientists' can provide their alternative remedy, but all I got was 'you are stupid, you are empty'. $\endgroup$– InformedAJun 5, 2016 at 1:07
Natural selection is the differential in survival and/or reproductive success among different individuals. As such, natural selection also refers to the process by which genotypes associated with greater fitness increase in frequency in the population through time.
More information on wikipedia > Natural Selection
An adaptation (or an adaptive trait) is a trait with a functional role that evolved (and is maintained) by means of natural selection.
More information on wikipedia > adaptation
Both the terms adaptation and natural selection are extensively used in science (and none of them come from the creationist religious belief). Their definitions are related as one is causing the other but these terms are not synonyms.
As the question is very introductory in the field of evolutionary biology, you might want to have a look at an introductory course to evolutionary biology. Evolution 101 (a.k.a. Understanding Evolution) by UC Berkeley is short, concise and very accessible even for those that have little a priori knowledge in biology.
You said "believe in evolution". It is of course a common phrasing from the creationist ideology. Evolution is a theory (a theory is very different from a hypothesis see this answer for more information) and therefore, the phrasing "to believe in evolution" sounds quite wrong as it wrongfully suggests evolution is a thing on which we could legitimately have different opinion about its existence.
2$\begingroup$ Great answer. To make things worse, in my language (and I reckon than in English too), the students use adaptation both as a noun and as a verb (to adapt), confounding it not only with "selection" but also with "evolution". $\endgroup$– user24284Jun 4, 2016 at 3:20