They can be used in similar contexts, but I get a different vibe from each of them.
Though both 手伝う and 助ける are translated as "to help," 手伝う sounds much more neutral. I would say it's more like "assist" rather than "help." For example:
家事で手伝ってください。 "Please help (assist) me with the housework."
In the case of 助ける, it sounds much more urgent and in some cases, it can mean "to rescue," rather than just "to help." For example:
事故が起こったから、怪我している人がいないように確認して、彼らを助けて下さい。"Since there has been an accident, please help them and confirm that there is no one injured.
This would be an instance in which I don't think you could use 手伝う and it would be more appropriate to use 助ける.
I hope this clears things up a bit. Let me know if you need further explanation.