pull ahead vs gain ground

pull ahead and gain ground both are verbs.

Word	Noun	Adjective	Verb	Adverb
pull ahead	No	No	Yes	No
gain ground	No	No	Yes	No

As verbs, pull ahead and gain ground are synonyms defined as:

Other synonyms of pull ahead include advance, gain, get ahead, make headway, win.

pull ahead (verb)	gain ground (verb)
obtain advantages, such as points, etc.	obtain advantages, such as points, etc.