Tasukeru - Save someone (from something dangerous, a dangerous situation) Tetsudau - Help someone, give a helping hand etc

I have heard both てつだう and たすける used in the same general situations, in which you are helping someone with a task. たすける can mean help in other more dire situations, but てつだう can never be used this way. Markus explained this as well, but I just wanted to add that both words can be used in neutral situations. To add to your vocabulary word, another word that you might use in more serious situations is: 救う　（すくう） - to save/rescue someone. This word is used in situations where someone is in danger. I hope this helped. Let me know if you need more assistance.