There is a huge difference in smoothness, which is actually pretty important. Every time any of my games drops below 40 FPS (which is quite rare since upgrading to my GTX 760), I feel like I'm playing a slide-show. This will be especially noticeable if you play competitive FPS, such as CoD. Even going from 40-ish FPS to 60 made a difference in my BF3 gameplay, and I was consistently getting better K/D ratio.
The numbers kinda make sense, but both AMD just recently changed their naming scheme. For NVidia cards, the first digit is the generation, the second and third digits as well as any suffixes (such as Ti) indicated the class of card. An example is NV's x80 series has always been their flagship single GPU - the GTX 480, GTX 580, GTX 680, and GTX 780 were all cards for the gamers who wanted the best single GPU they could find from their respective generations. The class of card is also important to pay attention to especially within the same generation - A GTX 670 is faster than a GTX 660, but the GTX 660 is faster than a GTX 750, because the 750 is aimed at a much lower class. AMD has a similar naming scheme. The first digit is generation, with the latter two digits representing a class. However, AMD's newest naming scheme also has prefixes and suffixes to pay attention to. Let's use the R9 290X as an example. The prefix isn't too noticeable as they only have a handful - R9 series are targeted at the serious gamers, R7 are mainstream, and the R5 are more entry level basic GPU's. The 200 means second generation (in reference to the architecture I'm assuming, as both the HD 7000 series and R 200 series are based on the same GCN architecture) and the 290 means it's the top dog and best AMD has to offer. The suffix serves to further differentiate within that class as often times AMD will have multiple classes from a single GPU core. Both the 290 and 290X are built on the same GPU (codenamed Hawaii), but the 290X is faster, as the 290 has some of it's cores disabled.
Now, as for video memory, 2GB is now the golden standard for 1920x1080 gaming as a lot of games are now utilizing more than 1GB of vRAM these days at that resolution. If you play older titles, or game at a lower resolution, or lower graphic settings, a 1GB model may not be a bad choice, especially if a 2GB model of the same card has a significant premium. Typically vRAM won't make a difference in performance... until it's 100% utilized, in which case performance tanks. Here is a quick explanation:
http://youtu.be/q0VNiWtQqb4?t=2m28s
Just to note, at the sub $100 price range, GPU competition is fierce, prices fluctuate a lot, and the price-brackets won't make a lot of sense, and there is just a lot of confusion in general. I wouldn't recommend getting anything less than Radeon HD 7770 (or R7 250x; same GPU). If you really can't spend $100, I would strongly advise saving up before buying a GPU.