what should be the diffrence between the diameter of a ball bearing and its housing ? and?

Question

and what should be the difference between the diameter of a shaft and its housing .

Answer 1

You must be talking about tolerancing. In this case you want your ball bearing to move without too much of rattling so my guess is that you'll need a clearance fit that is close to transition fit.

Follow the link below to look at the tolerance chart required.

Answer 2

The spacing should be enough for smooth relative motion but not large enough to cause slippage.