Counter - can switch in and kill the other guy or at the very least force it out
Check - can kill the other guy or force it out but cannot safely switch in
Example:
Togekiss counters Garchomp because of its immunity to Garchomp's stabs so it can switch in safely
Greninja checks Garchomp due to Garchomp's allergy to ice but cannot safely switch in unless it is very healthy
Note that these things do require prediction and a counter switching in can be killed off using a coverage move like how Garchomp can kill a Togekiss switching using stone edge
Source: https://gamefaqs.gamespot.com/boards/696959-pokemon-x/68613544#:~:text=A check is a Pokemon,and cause the aforementioned result.
