There's a difference, at least here in Canada, between 'cleared direct'
and 'cleared straight-in'. (I'm not sure if this applies to the US or
elsewhere...)

"Cleared direct [runway X]" is supposed to mean "Turn immediately toward
the threshold of [runway X]". This means that you will be off-centreline
for most of the approach.

"Cleared straight-in" is supposed to mean "Continue present course until
you intercept extended centreline of [runway X], then fly down the
centreline."

This is from a couple of instructors, including our Chief Flight
Instructor, and I've read it in at least one Canadian textbook. I can't
find anything in the AIP on a quick review, though.

Brian.
PP-ASEL/Night