The difference is subtle. It is the difference between causing something to happen (sometimes in a negative sense) and helping something to increase.
drive
4 [with object] (of a fact or feeling) compel (someone) to act in a particular way, especially one that is considered undesirable or
inappropriate.
4.3 Cause (something abstract) to
happen or develop.
‘the consumer has been driving the economy for a number of
years’
‘we
need to allow market forces to drive growth in the telecommunications
sector’
Source: Lexico —
drive
boost
1 Help or encourage (something) to increase or improve.
‘a range of measures to boost tourism’
‘A recent study in Costa Rica found that
preserving forest fragments around coffee plantations could boost crop
yields and increase income.’
Source: Lexico —
boost
Here are some examples from the Corpus of Contemporary American English:
Drive (swap in cause for drive):
Additional 5G phones, coupled with more carrier coverage, could drive sales a bit as well in future quarters.
MAG
TechCrunch
It was just one part of the massive effort by the pharmaceutical industry to drive sales of antidepressants, antipsychotics and other
psychotropic drugs to treat poor children, often for uses never
approved by federal regulators.
NEWS Denver Post
It suggested they did expect that they could count on this conspicuous conservation effect to drive sales.
WEB
Freakonomics
More
examples
Boost (swap in help increase for boost):
I thought some extra holiday cheer might boost sales.
FIC Analog Science Fiction & Fact
It’s that kind of enthusiasm retailers hope will boost sales in what is sure to be a tough holiday shopping season.
SPOK CBS
News
I agree that ebooks and mp3s have helped boost sales for a lot of writers and musicians, but it is also easy for that source of income
to end up online for free as illegal downloads (much to our
dismay).
BLOG David Gaughran
More
examples
UP
ISMORE
semantics). The other one is the shepherd metaphor; sheep are stupid and must be driven by someone, usually by fear, to where they can be sheared or slaughtered profitably (goats, by contrast, are smart and must be led to the same fate).