This is actually a very simple question.
1) /The table is clean./ means /The table is not dirty/. Clean and dirty are adjectives. Painted and unpainted are also adjectives. Read on.
By substitution, we can use any adjective to describe the table: The clean ~ dirty ~ painted ~ unpainted table is the one over there.
Here we see adjectives are either "stand-alone" adjectives or participial adjectives, -ing or -ed.
Note: the simple past one can be irregular: the *stolen book. Painted and unpainted here are used as adjectives taken from the verb paint.
2) /The table is painted/ could conceivably be a passive verb EXCEPT for the fact that one would not normally use a simple present passive here. Consider:
A) /The table is painted [by the man every week]/. The man in question would have to be rather neurotic to be painting the same table every week!
That said, one can easily imagine:
B)/The house is swept every day/ [by someone].
By the same token, /The table is cleaned [by some person]/ follows the same pattern: A passive voice in the simple present tense.
Summary: In many cases, only the context or speaker intention will tell you whether in a sentence like /The house is swept/ or, as in your example, /The table is painted/, the is + verb is being used as an adjective or as a verb. On its face, there is no way to determine which case applies: a verb or state or condition (adjective).
Yes, the grammar does change the meaning: /The table is cleaned/ with an implied agent (cleaned by someone) simply does not mean the same thing as /The table is clean./ A table could be cleaned by someone and its condition or state might still be dubious whereas in /The table is clean./ there is no doubt of its state.
The ambiguity created by a simple passive verb versus an adjective stemming from a participial adjective, one simply cannot say without further context which meaning is intended./The hut is swept/, adjective or verb?
BOTH, unless further elucidated:
The hut is swept every day by the kids.
The hut is swept and needn't be swept again. A swept hut is a clean hut. Yes, it is a cleaned hut.