spill vs brim over

spill is a noun but brim over is not a noun.

Word	Noun	Adjective	Verb	Adverb
spill	Yes	No	Yes	No
brim over	No	No	Yes	No

As verbs, brim over is a hyponym of spill; that is, brim over is a word with a more specific, narrower meaning than spill:

Other hyponyms of spill include overflow, overrun, run over, well over.

spill (noun)	brim over (noun)
the act of allowing a fluid to escape
a sudden drop from an upright position
a channel that carries excess water over or around a dam or other obstruction
liquid that is spilled

spill (verb)	brim over (verb)
reduce the pressure of wind on (a sail)	flow or run over (a limit or brim)
reveal information
cause or allow (a solid substance) to flow or run out or over
pour out in drops or small quantities or as if in drops or small quantities
cause or allow (a liquid substance) to run or flow from a container
flow, run or fall out and become lost