2 meanings?

Without further context, "Pack my cart." would typically mean: put things into my cart, say, by a salesperson at a store.

In US English there is no such phrase as "box my cart."

Anonymouspack my cart

It means pack things into my cart, or said differently, pack my cart with things. (I think you may mean "car", but the idea is the same either way.)

There are a number of verbs that are used in both patterns.

spread butter onto the bread / spread the bread with butter
spray paint onto the wal

CalifJimspread butter onto the bread / spread the bread with butter spray paint onto the wall / spray the wall with paint load the chairs into the van / load the van with chairs

Are clauses which are before the slash in the conative case and those after the slash in the instrumental one?

English does not have such an elaborate case structure, so no. The only reason you might want to work out the English usage in that way is if you have to find the equivalent in another language to do a translation.

In English we call these pairs "alternations".

CJ

CalifJimEnglish does not have such an elaborate case structure

Thank you for the reply.