If the same form is filled out and you have that activity pushing to SFDC as an activity, then it will list the name of the form, regardless of which page it was filled out on.
Yes, global forms are great! At my old company we started with local forms and then we decided to change our form qualification questions...which meant redoing all the forms, ugh. At that point we switched to global forms. I wish we had done that from the get-go.
When you say "in Salesforce" do you mean in MSI? You can include the program name or landing page to differentiate. You can also change your MSI triggers to be based off of program status change instead of the form fill.