In the context of retaining possession of something they can essentially mean the same thing. 'To hold on to something': to retain possession of it; basically implying that your doing it temporarily, perhaps as a favour for a friend 'He said I could keep it': in this context it is implied that 'keep' is more permanent. An exception would be 'I kept it', meaning I was keeping hold of it, but i no longer have to. In my last example I showed how the two words can be used in conjunction with each other. e.g 'To keep hold of something': basically the same as the very first example of keeping hold onto something. Finally there is one case where 'hold' can be used but keep can't, and it is in the context of 'hold' being used as a grasping action. Where you are physically containing something in your hand, 'I am holding a book'. Hope I could help :)

'Hold' means to have in your possession, or more specifically, in your hand or hands. 'Keep' followed by a noun means to retain. If you keep something, you don't lose it, give it away, throw it away or sell it. You keep it. 'Keep' followed by an adjective means to remain e.g. keep quiet. The only instance I can think of where they are interchangeable are in the set phrases 'Keep still' and 'Hold still', which do have the same meaning. Both verbs can also combine with other parts of speech, but always with different meanings. For example 'Hold on' means 'Wait', while 'Keep on' means 'Continue'.