What is the term for symbiosis in which one of the symbiotic organisms lives inside the other?

Endosymbiosis describes a specific type of symbiotic relationship where one organism lives inside another. This relationship can be beneficial to both parties involved, detrimental to one while benefiting the other, or neutral for one partner. The most notable example is the theory that mitochondria and chloroplasts originated as free-living prokaryotic organisms that were engulfed by ancestral eukaryotic cells, leading to a mutually beneficial relationship that has persisted through evolution.

In contrast, while mutualism, commensalism, and parasitism define other forms of symbiotic relationships, they do not specify that one organism resides within another. Mutualism involves both organisms benefiting, commensalism involves one organism benefiting without affecting the other, and parasitism involves one organism benefiting at the expense of the other. Therefore, endosymbiosis is the precise term for the scenario described in the question.