Is 'price hike' synonymous with 'price rise'? Since my childhood I have a belief that in economics price rise and price hike synonymous with each other.
Moreover, the Collin dictionary strengthens by belief:
Hike
But what you experts have to say--- are they absolutely same?
Yes there are used interchangeably in the literature e.g. see the occurrences printed in Mankiw Principles of Economics. For example, on page 509 its used completely interchangeably:

If a Pennsylvania gun manufacturer raises the price
of rifles it sells to the U.S. Army, its price hikes will
increase...

Price hike is also not special economic jargon, it is used pretty much consistently with dictionary definition.

A hike is a sudden or large increase in prices...