In a sense, they are similar, as they both affect how well a player plays. There's quite the difference though, GS affects how well, while Stamina affects how long.
GS - the better the GS the better a player plays. If there were two players with the exact same skills but one what at 7 GS and the other at 9, then the one with 9 would play better. In simple terms you can think of GS as a booster or multiplier of your player's current skills. Keep in mind it will apply to all (2 or 3) games that week.
Stamina - the higher it is the longer a player can play a match at their current level. So stamina has a max level of 9 (iirc) and it slowly decreases as the season goes by, the higher it is, the faster it decreases (so I've heard). The higher the stamina, the longer your player can play without a degradation in his performance. Example: Player 1 with 9 stamina could go all 48 minutes and his performance throughout the game will stay roughly the same, meanwhile, Player 2 with 3 stamina could go all 48 minutes but as the game progresses you will notice more missed shots, more turnovers, less rebounds etc. This is the degradation in performance
Hope that helps!