I am not completely certain, but I think you always get the basic version of each spell automatically, right up to level 50. However within a few levels most spells are seriously underpowered, and I don't think there are really "new versions" per-se (Like level 4 firebolt, level 13 Fireball, level 19 Uber-Firebolt). Instead you have to find, craft, quest for, or buy Apprentice, Journeyman, or Master versions of the spell.
So you will only have 1 "firebolt" your entire career, you just upgrade it repeatedly. Also it will always do the same thing, so if the one you got at level 2 does direct damage only then that is all it will ever do, and that will be your only Fire based DD you ever get. However at level 7 you might get a "Bonds of Fire" spell which does slightly less damage than a firebolt but also slows the target a little. It will need to be upgraded as well then, but you will never get another Fire based DD+Slow again, or if you do it will be a more powerful version that you get ONLY because you chose a class at level 10 or a sub-class at 20 that specifically gets more powerful versions of that kind of spell.