The generic term for a structure inside a cell that forms a separate functional compartment is organelle.

Organelles are membrane-bound structures within eukaryotic cells that perform specific functions. They are like tiny organs within a cell, each with its own specialized role.

Here are some examples of organelles:

* Nucleus: Contains the cell's genetic material (DNA)

* Mitochondria: Responsible for energy production (ATP)

* Golgi apparatus: Modifies and packages proteins

* Endoplasmic reticulum: Involved in protein synthesis and lipid metabolism

* Lysosomes: Digest cellular waste and foreign materials

* Chloroplasts (in plant cells): Perform photosynthesis

While organelles are generally considered to be membrane-bound, some structures like ribosomes are not enclosed by a membrane but are still considered to be functional compartments within the cell.