They are never synonyms. Maybe you could provide some context so we can understand better where the confusion comes from? In linguistics, "object" refers to the argument of most transitive verbs. I have not heard linguists use "objective" to turn this sense of "object" into a noun.

I have heard people who speak Mandarin Chinese as a first language use "the objective" to refer to the object of a verb (and similarly "the subjective" to refer to the verb's subject), but this is an error, as far as I can tell. I haven't heard linguists use this terminology, including linguists whose first language is Mandarin Chinese.

If all you want is a simple synonym you might be better off looking at a thesaurus or synonym list.

object = objective
The goal intended to be attained (and which is believed to be attainable)

The difficult with this question, Nima, is that the assessment of whether X and Y are (near-)synonyms for some speakers depends on the context of the utterance. A word in isolation makes it impossible to assess anything.

for example, 'two' and 'a couple' and 'pair' can mean very similar or very different things in various contexts.

Good luck.