Is 'price hike' synonymous with 'price rise'?
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...