I would suggest that a distinction can be made in that a trilateral
agreement is one which bestows the same rights and obligations on all
three parties, and implies a degree of equality of the parties in the
matter at hand. A tripartite agreement does not necessarily do so.
You can see this if you consider a specific example, the
Britain–India–Nepal Tripartite Agreement.
The agreement concerned the status of Gurkhas following the
independence of India. The actual content of the agreement in detail is
not relevant here, the point is that only a Nepalese citizen can become
a Gurkha - it is not as if it regulated the rights of British or Indian
citizens to become Gurkhas. Therefore it is not a trilateral agreement,
but a tripartite agreement.
Does the notorious Tripartite Pact of 1940 between Germany, Italy and
Japan fall in the same category? Good question. Well, none of the
parties considered themselves as equals of each other, let alone anyone
else. Rather Japan agreed to recognize Germany and Italy together as the
leaders of the New Order in Europe, and vice versa - if anything, a
bilateral agreement between Germany-Italy and Japan.