Hi Groggy Grognard!
There are quite a few changes between FS2 (the various versions) and the FSR (which is a 3rd edition in all but name).
I recently answered the same question elsewhere, and since I'm in a bit of a hurry, I'll copy-paste it here. Hope this helps
From memory, the major changes are:
-FSR has no opposed Spirit characteristics (from Extrovert vs. Introvert, Passion vs. Calm, & Faith vs. Ego in FS2 to Presence, Faith, & Will in FSR)
-FSR VP calculated by dividing the rolled number by 2 instead of by 3
-FSR has a new mechanic in the Defense characteristic. Defense is subtracted from attack VP scored against the character. This replaces defensive actions and thus greatly speeds up combat.
-FSR has introduced Fighting Stances, which are a set of basic approaches a character can choose to take in combat.
-In FSR, Martial arts actions have been redone with greater focus on styles and less clutter in the rules. You now buy a style to get the base bonus/action, and you will qualify for further bonuses/actions if you have the required skill ranks (typically, the higher Fight/Melee/Shoot you have, the more features of the martial arts style you'll qualify for)
-Weapons, gear, and other 'stuff' has been greatly expanded in FSR. Weapons have some brand new features called 'properties', and armors that are not built specifically to withstand said properties have reduced effects. (i.e. a fire-proof suit receives full armor protection vs. Flame weapons, but not vs. Slug guns). There are many more examples of things available for purchase, which were written in an attempt to sneak more setting and fluff into the game. Tech Level is discussed at length.
-FSR occultism has been expanded with more background info, and a few new powers invented (Eskatonics now finally have a rite with which to fight Symbiots)
-In FSR, critical failures may occur when a natural 20 is rolled (which is also a natural failure). Critical failure is determined by rolling another d20, a score of another 20 resulting in a fumble.
-FSR allows characters to spend Wyrd to gain re-rolls. (1 for one)
-FSR has rules for such things as Falling/Impact/Collision, Heat/Fire/Plasma, Asphyxiation, Decompression, and Radiation.
-There might be more major rules updates, although these are the ones I can think of right now.
In addition, there are loads of minor new rules throughout.
Vi also added loads of optional rules to suggest ways of tweaking the game to fit the style of individual gaming groups.