Is there a difference between Sigma and Black?
There are differences, albeit a lot of minor ones you won't really care about if you play the games casually. Basically, in Sigma:
-intro movie was removed
-the first chapter's scenery was vastly changed from a rocky waterfall to a lush forest
-3 required chapters exclusively using Rachel were added
-enemy layouts were changed; some enemy spawns were removed or added; mostly the same though
-some visual effects and enemy designs were changed
-some puzzles were changed or removed and water running was more streamlined and made easier to do
-added some new enemies and bosses like guys on motorbikes, blue will-o-wisps, mermen, Alternator, Gamov, etc.
-Dragon's Claw and Tiger's Fang (Dual Swords) are useable for the first time in Sigma
-Golden Scarab rewards were changed
Generally speaking, the differences are kinda minor that if you aren't like a Karma Runner or purist or anything, you might not care too much about how different they are. It's a much more similar experience than Ninja Gaiden II to Sigma 2 anyway.