how come a role can see a transaction field on purchase order, but not in a search

Can you give an example? I have found that I typically have the incorrect field name selected when populating a sarch.

i created the search and as an admin i can see it. but when another role runs the search they dont see that column in results

That may not be available as it is dictated by their role. I was able to edit our roles to include certain items and custom fields to show. th best place I found to edit all if this was under the role --> Forms --> Custom Record. I would start there.

even though this is a custom transaction field?

Yes. You can scroll down the very extensive list and any custom field is noted. For Example: Vendor Approver (Custom field)