Do the 1975 dt175 and 250 share the same exhaust?
Thanks for any help!

Doesn’t appear that is the case. 250 is probably longer and mounting looks different. Part numbers are definitely different. Parts sellers such as partzilla, Rocky Mountain and cmsl have the parts lists and schematics to check for yourself. 

model numbers are different in the part number but the actual part number is the same
dt175 443-14610-01-00
dt250 498-14610-01-00.

"model numbers are different in the part number but the actual part number is the same
dt175 443-14610-01-00
dt250 498-14610-01-00."

In this case, it is the first three characters of the part number that are important - they determine the model that a part was originally fitted to.

The next batch of five characters relate to the part type, so I would expect to see the same for most exhausts.

If you get the chance, download any genuine Yamaha parts or service manual (find these in the Tech Library) and in there you will find instructions on how to "read" Yamaha part numbers. I've found that early manuals have the most comprehensive instructions and they are usually found at the front of parts manuals and the back of service manuals.

I would be very surprised if the 175 and 250 shared the same exhaust.

They are not the same.  Gr8uncleal is absolutely correct on the part number decoding. 

Even a modern Yamaha two stroke uses -14610- as the exhaust part number...  look up a YZ85 exhaust.  Model code prefix is critical