Opposition is usually to describe a force/person/group of people acting against something. E.g. The opposition argued against the suggestion. Objection is usually to describe an idea or argument spoken or thought against another idea or argument.

What is a reply to an objection?

The judge then makes a ruling on whether the objection is "sustained" (the judge agrees with the objection and disallows the question, testimony, or evidence) or "overruled" (the judge disagrees with the objection and allows the question, testimony, or evidence).

How does trademark opposition differ from trademark objection?

Trademark objection is the objection raised by the Examiner of Trademarks whereas Trademark opposition is an opposition proceedings initiate by the third party. The third party here means any person present in public that may have objection towards the acceptance of your mark.