I'm putting the children on the bed vs I'm putting the children in bed.

Put in bed. Why do not we use a definite article here?
Put on the bed. Why do we use a definite article here?

in BrE, we normally put young children to bed. They are then in bed.

These can be taken as fixed expressions which have more to do with sleeoing than destination/location.

@sadra1400 - Please remember to put the words/phrases you're asking us about into complete sentences every time.

'In bed' means they're tucked under the covers as a precursor to them going to sleep for the night (or a nap). As 5jj mentioned, it's really about preparation for sleep.

'On the bed' does however refer to actual location. We don't know what the purpose is for placing them there.

Here the father repeatedly puts the children on the bed in a valiant effort to get them all dressed. Nobody is sleeping or preparing for sleep, although I imagine the dad might enjoy a nap after that.

Mom seems to have a rougher time of it, despite the help (or lack thereof) from the cat.