Difference between "underneath" and "under" when we describe an action

I ask for the difference in a sense of active quality rather than a stative quality of the verbs. E.g. in "the toy is sitting underneath/under table", the verb is stative. So we are dealing with adverbs.

For example, is it correct if I say :

I will slip the envelope underneath the door.

or should I say

I will slip the envelope under the door.

"It's sitting underneath the table" is not stative - it's still an action. Stative is, like "it understands underneath the table" or "it tastes under the table."

"I slipped it underneath the door" implies it stayed under the door. A door is a thing that is not very wide, and "underneath" would be inappropriate.

"I slipped it under the floor" and "I slipped it underneath the floor" would be the same thing, although I would want to use - incorrectly - "to underneath", indicating that "underneath" is a concrete place, whereas "under" is a position. However, I live among non-native speakers who use that construction, so I probably see a non-obvious logic.

"Under the sea" tells me it's in the water, whereas "underneath the sea" is a place below the water.

As for julio's comment, although it's true you wouldn't really say "it's not over it, but under" (realistically) - you can say "it's not over it, but underneath it."