That's correct, the game seed is the numbers in the file name. You can also set it to be a specific number when you create a new farm, in the advanced options in the farm creation menu.
Basically it's a number that influences some of the "random" stuff in your game.
The way that randomness is calculated on Switch is somewhat different from PC, so you won't get the same results on Switch versus PC with the same seed. Mobile calculates random stuff the same way though, as far as I know, so if you use the same seed you should get the same results on mobile and PC
for stuff determined only by the seed.
That caveat is important because there are random things that are determined by other inputs as well as, or instead of, the seed. For example, daily luck is based on seed, step count, date, and some other stuff, so you probably won't have the same daily luck between two files even if you use the same seed. On the other hand, geode contents, monster floors, and the traveling cart are all based only on the seed, so those will be consistent if you use the same seed. Pretty much anything predicted in
the Stardew Predictor website is based only on seed.