boundary vs upper bound

boundary and upper bound both are nouns.

Word	Noun	Adjective	Verb	Adverb
boundary	Yes	No	No	No
upper bound	Yes	No	No	No

As nouns, upper bound is a hyponym of boundary; that is, upper bound is a word with a more specific, narrower meaning than boundary:

boundary: a line determining the limits of an area
upper bound: (mathematics) a number equal to or greater than any other number in a given set

boundary (noun)	upper bound (noun)
the greatest possible degree of something	(mathematics) a number equal to or greater than any other number in a given set
the line or plane indicating the limit or extent of something
a line determining the limits of an area