What is the difference between 'in the bed' and 'in bed'?

Solution 1:

In bed refers to customary activities undertaken while someone is (usually) on the way to sleep.

In the bed is normally less likely to denote customary activity associated with sleeping and more likely to denote other activities:

I found cracker crumbs in the bed

This would describe something that might have taken place while gathering bed linen for the laundry. It also might have been someone else's bed, not your own.

I found cracker crumbs in bed

This would probably mean they bothered you while you were trying to sleep.

Solution 2:

If you say that you "read in the bed," you're referring to a specific bed in which you read. If you say that you "read in bed," you're making a general statement that you read in whatever bed in which you find yourself.