circle of curvature vs osculating circle

circle of curvature and osculating circle both are nouns.

Word	Noun	Adjective	Verb	Adverb
circle of curvature	Yes	No	No	No
osculating circle	Yes	No	No	No

As nouns, circle of curvature and osculating circle are synonyms defined as:

circle of curvature and osculating circle: the circle that touches a curve (on the concave side) and whose radius is the radius of curvature

circle of curvature (noun)	osculating circle (noun)
the circle that touches a curve (on the concave side) and whose radius is the radius of curvature	the circle that touches a curve (on the concave side) and whose radius is the radius of curvature