At the Historic Houses Trust of NSW, we have twelve sites and most have
public programmes and most have objects of the third type you describe:
items  that might be purchased or gathered for public activities for school
groups, demonstrations, objects for hefting, smelling, et cetera. We
catalogue these items in a "Props" register that is kept at each property
along with the typical cataloging documentation such as photos, invoices,
donation letters and so on.

This props register is kept separately from the objects catalogue for the
property and the entire Historic Houses Trust collections. The props are
numbered or marked in some way with a "P" and sequential number. For
example, a cooking pan and lid  might be P54:1-2.

I can recall that the "Art Newspaper" reported that a number of props that
were made in the early 20th century for an interpretation exercise at
Pompeii and Herculaneum slowly but inevitably became part of their original
collection.

More info, contact our very efficient Collections Management Unit.

MBogle