In 1948 both a Manhattan and standard are sedans. In 1951 the Manhattan was a hardtop.
Some differences between the '48 Manhattan and standard:
Manhattan has fancier interior and had front and rear seat arm rests, chrome strips on the door panels.
Two barrel carburetor
Chrome inside window frames
Chrome strip across the center of the dash
Larger tenite color coordinated steering wheel, shift lever knob and signal light lever knob.
Enclosed steering column
Wider rocker panel chrome trim
Many were tutone
Manhattan badge on the fender flanks
There are more differences so hopefully someone can chime in with those.
For some reason, the general population always seems to call any Frazer a 'Manhattan' and perhaps the person who sold you yours did so as well. It is notable how many Frazer standards are listed on line as "Frazer Manhattan"
The standard is a good car so don't worry about that. The Manhattan is the upscale model with said features and some others.