I'm honestly surprised this isn't better understood in this community, at least as an approach to the tree of life system of classification, with or without its merits. I didn't go to college and went to public school that suppressed science education, but this was how I came to understand evolution and that all types of life had a universal common ancestor.

I'm not speaking to the accuracy of the meme, and the science community at large has its criticisms of cladistics, but I'm not sure I would classify this as a problem of biology or language, or a problem at all. It is the most common method of evolutionary classification at this time.

Keep in mind I'm a blue collar worker on my lunch break and not a scientist nor college educated. I just like to learn in my free time about a bunch of stuff.

Pretty much. It helps if you think the word "dinosaur" has two partially overlapping meanings:

1. Cladistic: every single descendant of the last common ancestor between the triceratops and a duck, including both. Plus pretty much any bird.
2. Popular: a bunch of extinct animals like the T-Rex, velociraptor, triceratops, etc. Plus animals visually resembling them, regardless of cladistic classification. Notably, it does not includes Aves aka modern birds.

So for example. Turkeys would fit #1 but not #2. Depending on the person, dimetrodons and pterosaurs would fit #2, but not #1 [see note]. A T-rex would fit both.

NOTE: pterosaurs aren't from the clade Dinosauria, but from a distantly related clade called Pterosauria. Dimetrodons are synapsids so they're closer to us mammals than to Dinosauria.

the cladistic approach developed for a reason

you know, two organisms might look similar at first, but what's often more important is the set of internal features, such as biochemistry, tolerance of toxins, etc.

if you take all these internal features, you find that they're well-preserved within evolutionary groups; but not within groups that merely look alike