I get that of course if different projections are utilised, the images will look different.Gerald,
Visually, yes, there would be if a projection type other than rectilinear is adopted, or if the horizontal and/or vertical compression feature in, for example, PTGui is adjusted. However, these features are not without issues of their own.
EDIT: In addition, if an image is produced via nodal stitching rather than shift stitching then the images will differ visually - I think - given that the former represents a 'faceted' image whereas the latter preserves rectilinearity, just at a larger size than the sensor is capable of natively.
Cheers,
But there's nothing stopping you re-projecting a single shot from a wide angle lens.
Still scratching my head as to why, unless you want the extra resolution, you'd ever make the choice to stitch multiple images from a longer focal length.
Kind regards,
Gerald.