make headway vs pull ahead

make headway and pull ahead both are verbs.

Word	Noun	Adjective	Verb	Adverb
make headway	No	No	Yes	No
pull ahead	No	No	Yes	No

As verbs, make headway and pull ahead are synonyms defined as:

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

make headway (verb)	pull ahead (verb)
obtain advantages, such as points, etc.	obtain advantages, such as points, etc.