The primer is to give good adhesion to the material. Hence different ones
for wood and metal, etc. Undercoat at one time was always near the same
colour as the top coat but less expensive, so made the job slightly
cheaper than using two or more coats of top to get the depth of colour.
But things are a bit blurred these days. ;-)

What Dave said.

The need to achieve a good bond is still with us, but modern paints have
such good covering power they make undercoat almost superfluous.

Dave