For example, “flammable” and “inflammable” both describe an object that can easily catch on fire. I can also think of “ceased” and “deceased”, both of which can mean someone or something has been brought to an end.
edit: Some people are including words that can also mean its opposite (like sanction or table), those are cool too! The more weird words, the better!
Dust. Dust the shelf, dust the loaf with flour.
Well, this is the opposite thing (same word meaning opposite) but if you ask me it’s the same.
EDIT: For some that fit better:
Caregiver/caretaker is a fun one I had never considered.
I think valuable / invaluable actually have different meanings. Something which is invaluable, is so important a value should not be assigned.
Valuable member of society
Invaluable member of society
Neither case leads to a tangible valuation of the member as both have positive meanings. Invaluable is sort of like valuable+1, but both are just invaluable superlatives.
invaluable would be equivalent to priceless.
Priceless and worthless mean the same
Don’t @ me
That’s called a contronym, which (as you said) is different than what OP is looking for
https://en.wikipedia.org/wiki/Contronym