on time vs punctually

on time is an adjective but punctually is not an adjective.

Word	Noun	Adjective	Verb	Adverb
on time	No	Yes	No	Yes
punctually	No	No	No	Yes

As adverbs, on time and punctually are synonyms defined as:

on time (adjective)	punctually (adjective)
acting or arriving or performed exactly at the time appointed
payable in installments within a designated period of time

on time (adverb)	punctually (adverb)
at the expected or proper time	at the expected or proper time