An earlier answer, insectarium for living insects, satisfies your parallels with living bees (an apiary) and animals (a zoo or menagerie). That is,
A place for keeping and breeding insects; an entomological vivarium.
The insectarium, however, is a curated collection of living bugs.
For displays of collections of dead bugs (entomotaxy), two terms satisfy your parallels with taxidermy (diorama) and philately (album). Those terms are combinative (just as are taxidermological diorama and stamp album), but in the appropriate context the terms may be used to good purpose without prepending the combining term insect:
As suggested by the usual meanings of box and cabinet, the former is usually associated with a smaller scale, more temporary display and arrangement of bugs (or a subdivision of a cabinet), and the latter with a larger and more permanent display.
Here is a general description of an insect-cabinet, from Directions for collecting and preserving insects (A.S. Packard, 1873):
Insect-cabinet. For permanent exhibition, a cabinet of shallow drawers, protected by doors, is most useful. A drawer may be eighteen by twenty inches square, and two inches deep in the the clear, and provided with a tight glass cover. For constant use, baxes made of thin, well-seasoned wood, with tight fitting covers, are indispensable. For Coleoptera, Dr. Leconte recommends that they be twelve by nine inches (inside measurement). For the larger Lepidoptera a little larger box is preferable. Others prefer boxes made in the form of books, which may be put away like books on the shelves of the cabinet, though the cover of the box is apt to be in the way.
The style and details of insect-box and insect-cabinet construction and appointment vary widely.