To put it simply, a Blanket Check is a Pokémon that checks multiple threats and trends in a tier. For example, Chansey is a solid example of a Blanket Check because it solidly Checks/Counters many Special Attackers such as Dragapult and others (Even though it is in UU). And just like I stated above, the difference is a matter of 1 Pokémon vs. Multiple. Also, to be clear, Blanket Checks are designed to be able to check multiple threats like I explained with Chansey, not like just being able to check a couple of Pokémon.
Hope this helps!