Are they synonyms for looking back on the past that have separate contextual applications or do their meanings differ?
"Retrospect" quite literally means "look back" in Latin and retains it's meaning in English.
According to Marriam-Webster, hindsight (noun) is
perception of the nature of an event after it has happened In hindsight, it's clear there were alternatives. Hindsight is twenty-twenty.
while retrospective (noun) is
1a(1) : of, relating to, or given to retrospection
(2) : based on memory a retrospective report
b : being a retrospective a retrospective exhibition
2 : affecting things past : retroactive retrospective laws
3 : relating to or being a study (as of a disease) that starts with the present condition of a population of individuals and collects data about their past history to explain their present condition
where retrospection (noun) is
the act or process or an instance of surveying the past
Retrospection can have a more complex meaning compared to hindsight.
You might say
In hindsight, I shouldn't have eaten the cake.
Retrospectively I shouldn't have eaten the cake.
Hope this helps.