If I show you some examples of the above words it might help:
1. "Our team had a great success last weekend, when we beat the current champions." Success here means to win or to have some sort of victory. It could be in sport or other areas such as work, education etc.
2. "Catherine is succeeding Lucy as the new Head of Training." The meaning here is that Catherine is the new boss, she is taking over from Lucy. However succeeding can also have a similar meaning to success, that's maybe why it's rather confusing!
I hope that helps!