Not sure why you're making this so hard for him.
Let's take Ati cards as an example.
The first number is the generation, newer generations mean more features (not necessarily faster) but you need to take the whole set of numbers in to consideration.
Example, a 7770 would be a current generation card, whereas a 6970 would be a last generation card. However, the 6970 is faster than the 7770 due to where it sits in the range. A 7770 is the lowest of the 7xxx series but the 6970 is highest of the 6xxx (single gpu) series.
The only way to know for sure where a card sits in relation to another card is to look up benchmarks. There are a few comparison sites that list all GPUs in order with approximate performance metrics.
It did get a bit confusing on the nVidia side a few years ago though.
They used to have 6900GT, 7900GTX etc etc, then they went to GT250, GTX670 etc for example.
Clock speed and RAM are not a good indicator of performance, for example:
An AMD (ati) 6670 2GB card would be worse in games than a 6870 1GB.
Where we have problems is when a game box says "nVidia GTX470 or equivelant". How are you supposed to know what is equivalent? Well, you can't just by reading the numbers. You may think a GT610 is better than a GTX470 right? Wrong! The GTX470 would eat it for breakfast.
So, the only way to can know for sure that one card is faster than another is either if the numbers at the end are higher within a range. Eg 7970 is faster than 7770. GTX670 is faster than a GTX660, or if the card you are replacing now costs about the same or more than what you paid for your last card. Eg, a £250 card today will be much faster than a £250 card for 5 years ago.
Comparing between manufacturers is something you just have to research and find out for yourself.
Also, with regards to minimum specs on game boxes. They are MINIMUM specs to RUN the game. Whether you can actually PLAY the game is another matter entirely. Take Crysis3 for example:
Minimum spec for Crysis3 GPU is listed as: DirectX 10 graphics card with 1 GB RAM, Nvidia 400-series or AMD Radeon 5000-series.
So, chuck an nVidia Geforce GT610 in an you're good to go? Wrong! It will be a slideshow even on the lowest graphics settings. Stick a GTX470 in there and you might be able to play it.