Ok, basically, how it works is that the "x00" digit in the card for Nvidia indicates the "generation" that card was released in. The higher the x00 digit, the
newer the card. The 0x0 digit indicates how fast the card was
within the generation. A fast card from an older generation can still be faster than a slow card from a newer generation. For example, a Geforce GTX 680 is faster than a Geforce GTX 750. But if the 0x0 digit is the same and one card is newer with a higher x00 digit, you can generally trust that the newer card is faster. So a Geforce GTX 780 is faster than a Geforce GTX 680. Right now, the newest, fastest Nvidia graphics card is the Geforce GTX 980.
AMD graphics cards are similar; up until recently they used four digits. The x000 digit indicates generation, the 0x00 digit indicates how fast the card is within that generation, and the 00x0 digit is used to indicate further how fast the card is within that. So a 7970 is faster than a 6970, which is faster than a 6870, which is faster than a 6850. But a 6950 is faster than a 7770! A year ago, they switched over to a three-digit format like Nvidia, starting with a 200 series. Right now the fastest AMD graphics chip is the R9-290X.
If you want to dig past naming schemes, it gets a bit hard to compare graphics cards. You CANNOT simply compare specifications like clock speeds or memory size. The easiest and most accurate way to compare graphics cards is by looking up "benchmark tests" on tech review websites like Anandtech.com, Techspot.com, Techreport.com, and many others. "Benchmark tests" use methods, including but not limited to frame rate monitoring, to objectively measure how smoothly various graphics cards play games in comparison to each other. The higher the frame rate a graphics card gets in a game, the smoother it should play (but there can be other factors...which are rather technical).
A good summary of tips in looking for a graphics card can be found here:
https://www.youtube.com/watch?v=c3BKuNXdM5A