Help me is a general request can refer to anything. And help me out relates to something you are doing and you request someone to assist you in doing it.

As others have said the meaning is near identical, however I would add one idea in relation to context. I think 'help' is very general and can be used in all situations, while 'help out' has a couple of ideas attached to it (for me at least) one is that you will not be helping alone. You may be helping me, or another person, or even a team of volunteers etc. Consider: Can you help me with this problem? (May imply: Can you do it for me) Can you help me out with this problem? (Probably implies lets fix it together) These are only my perceptions and so they are my personal differences in usage and understanding. And in reality in either situation they are completely interchangeable!!!!

thanks for your help

To begin with, your question should change the word 'different' for 'difference'. Then, I use them both as equals :)