maths vs applied math

maths and applied math both are nouns.

Word	Noun	Adjective	Verb	Adverb
maths	Yes	No	No	No
applied math	Yes	No	No	No

As nouns, applied math is a hyponym of maths; that is, applied math is a word with a more specific, narrower meaning than maths:

maths: a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
applied math: the branches of mathematics that are involved in the study of the physical or biological or sociological world

Other hyponyms of maths include pure mathematics, applied mathematics.

maths (noun)	applied math (noun)
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement	the branches of mathematics that are involved in the study of the physical or biological or sociological world