tally vs pull ahead

tally is a noun but pull ahead is not a noun.

Word	Noun	Adjective	Verb	Adverb
tally	Yes	No	Yes	No
pull ahead	No	No	Yes	No

As verbs, pull ahead is a hypernym of tally; that is, pull ahead is a word with a broader meaning than tally:

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

tally (noun)	pull ahead (noun)
the act of counting; reciting numbers in ascending order
a score in baseball made by a runner touching all four bases safely
a bill for an amount due

tally (verb)	pull ahead (verb)
determine the sum of	obtain advantages, such as points, etc.
keep score, as in games
gain points in a game
be compatible, similar or consistent; coincide in their characteristics