pseudometric space vs semi-metric space

pseudometric space and semi-metric space both are nouns.

Word	Noun	Adjective	Verb	Adverb
pseudometric space	Yes	No	No	No
semi-metric space	Yes	No	No	No

As nouns, pseudometric space and semi-metric space are synonyms defined as:

pseudometric space and semi-metric space: a generalized metric space in which the distance between two distinct points can be zero.

pseudometric space (noun)	semi-metric space (noun)
a generalized metric space in which the distance between two distinct points can be zero.	a generalized metric space in which the distance between two distinct points can be zero.