The drain trim piece that your talking about has to 'mate' with the (threaded) shoe that is already in place under the tub (assuming your not changing the whole waste and overflow?) You need to take it with you to a supply house to make sure that you are getting a new one with the correct thread size, 1 5/8 or 1 1/4 I believe are available, some other odd ball thread was used in older style tub drains but all are 1 1/2 tubular, with the exception of some older ones which had a 1 1/2 MIP thread that threaded into a FIP ftg...
If your buying the whole new drain it will of course be mated. You can check to see if you can find a bigger flanged type but Probably Your best bet is to get a brush and a good cleaner and clean the old rust off. Most tub drain flange pieces are real close to the same O.D....Good luck.
go to a plumbing supply house that sells to the plumbing trade. Usually the counter guys will have a ready answer. The older tubs (20 years ago or so) used these type drains.
Tubs are always made to accomadate an 1 1/2 drain, showers 2"...when it leaves the waste and overflow (1 1/2"), you can increase to 2" and follow up with a 2"trap, etc...but coming from the tub itself, I've never seen a 2" tub drain ??? 1 1/2" pipe measures around 2" ya know ...good luck