The differences are very subtle.
During the first chorus on the 45 she sings:
"talking 'bout a midnight, ohhhh, midnight affair we're gonna have a midnight, ohhhh, midnight affair",
At the same chorus on the LP take she sings it the other way around:
"we're gonna have a midnight, ohhhh, midnight affair talking 'bout a midnight, ohhhh, midnight affair",
The vocal phrasing and the intonation of the "ohhhh"'s etc are also different on the two versions.
Compare below. 45: https://www.youtube.com/watch?v=DtqvKpwduPk LP: https://www.youtube.com/watch?v=pvV6ZgANpLg