I did see a sign for rosy tetra at the LFS but they were sold out, as well as another "red" tetra. To be clear
You mean this is a rosy tetra
And NOT this "red" tetra right?
Correct. Common names can really be problematic, as they tend to vary from country to country, and even region to region, in many cases. Only last week in another thread, a member from the UK referred to "red neons" which in NA are called "cardinal tetra," never red neon tetra. I knew what he meant, but this is a very simple example of how confusing common names can be for many.
The lower photo in your post is a nasty little fish, a notorious fin nipper of almost anything else in the tank, unless kept in large groups, but even then
never with sedate or long-fin fish. I have seen this fish referred to as Serpae Tetra, Red Minor Tetra, Red Tetra...and probably other names if I could remember them all. The species is
Hyphessobrycon eques. Unfortunately, it is one of several species of tetra that have some very striking similarities, so it can get confused. The dark (usually black) oblong "shoulder patch" or "humeral spot" as it is termed, the black blotch in the dorsal fin, and the overall reddish colour (some species like the Black Phantom lack the reddish colour) are three identifiers. Often, but not always, there is some white in the dorsal fin. There are some 30 species in this "clade" that include the fish I have previously suggested, and obviously many others. Temperament and behaviours are similar for some of them, but there are exceptions like this Serpae Tetra.
If you look at the top photo in your post, the Rosy Tetra, you will clearly see that it has the same identifiers I mentioned in the preceding paragraph. But two species could not be more unlike each other in temperament that these two in the photos. I will post some links to the fish I earlier mentioned to be clear.
Rosy Tetra:
http://www.seriouslyfish.com/species/hyphessobrycon-rosaceus/
Roberti Tetra:
http://www.seriouslyfish.com/species/hyphessobrycon-bentosi/
Red Phantom Tetra [the photos here do not do this fish justice, I have a group of 15 and it is one of the most brilliant red fish I have ever seen]:
http://www.seriouslyfish.com/species/hyphessobrycon-sweglesi/
Black Phantom Tetra [not very colourful with angelfish, but a peaceful shoaling fish]:
http://www.seriouslyfish.com/species/hyphessobrycon-megalopterus/
I have kept all of these, some for many years, so don't hesitate to ask questions. The characins are also one area of particular interest to me.
Byron.