What is the difference between an orbital rim implant and a tear trough implant?

Tear trough implant is practically the same as lower orbital rim implant. Technically, the orbital rim implant would expand the whole lower eyelid area whereas tear trough implant is mainly the inner area but the terms are used loosely. The important points are you want to use silicone implant as much less invasive and also use transconjunctival technique.

A tear trough implant is a smaller form of a lower orbital implant that comes in standard sizes that sits in front the infraorbital rim closer to the nose that is used to treat what its name implies. A true orbital rim implant is custom made and sits along the infraorbital rim like a saddle and is used to treat various forms of vertical and horizontal infraorbital rim deficiencies. 

Tear trough is closer to the bridge of nose. Rim implant is directly under eye. Often both are necessary or one big one that treats both areas. Both treat volume deficiency in two slightly different areas.