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Wikipedia definitions for these terms are pretty similar:

They sound like the terms are synonyms. Why there are separate articles for them then?

Is it true that every person is a reptilomorph and an eupelycosaur just like he/she is a mammal?

Bonus question: what is the difference between a cladogram and a phylogenetic tree?

PS Please don't just give definitions and/or quote Wikipedia. Point out the differences, if any. Even better, provide examples that can be considered one but not the other.

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A taxon (Plur. taxa) is any (monophyletic or not) group of species. For example the group of yellow flowers is a taxon. The group of primates is a taxon. The taxon of aquatic animals is a taxon.

A clade is a monophyletic taxon or monophyletic group if you prefer. A monophyletic taxon (or a clade) is defined as a taxon that contains only all descendants of a common ancestor and the common ancestor. On the following picture, only the Taxon 1 is a clade.

enter image description here

To cite few examples of clades: Primates, Eukaryotes, Rosacea, Reptilomorpha, Rodentia. (The links yield to tolweb.org. See below for more info about this site)

A cladogram is some kind of reduced evolutionary tree that only shows the branching pattern but the length of the branches does not carry any information. At the opposite on a evolutionary tree the lengths of branches usually indicate the inferred time from the divergence.

I think the best tree you can find online is tolweb.org. You can find here the clade of Reptilomorpha and here the clade of Eupelycosaur. As you can see from these links, the mammals form a clade within the Eupelycosaur which itself is a clade within the Reptilomorpha. So yes, every human being is a Reptiliomorpha/Eupelycosaur/Mammalia. You can have fun going through this evolutionary tree and see what are the common ancestors between human and other mammals, human and turtles, human and jellyfish, human and plants, etc… to cite just a few relationships you might be interested to look at.

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+1 But I'd say, taxon is not any possible grouping, but a grouping proposed by someone. It's basically a formalized hypothesis about natural arrangement of species. (This natural can be understood in multiple ways.) In this respect "yellow flowers" do not make a taxon. –  har-wradim May 24 at 0:11

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