Welcome aboard Goose_green
Yep, a DD counts as a warship. A liner counts as a merchant ship. Basically, any ship whose function is combat would be a warship and any other ship would be either a merchant or a small merchant. Mostly I define small merchants as fishing boats and sampans.
If the count that you sent in is incorrect, please resubmit your report and I'll correct the one that is in line for completion at the moment.