Is the width of a 10-speed cassette the same as a 9? More specifically, will a 105 cassette fit on a Tiagra hub?

Cheers.

Strangely a 10 speed cassette is narrower than a 9 speed. Yes it will fit on a nine speed freewheel, just remember to fit the spacer that comes with the cassette.

Really? I'd have thought it'd be the other way around.

No you need the spacer! If you put the cassette on without it the freehub siezes up. (Apparently, I wouldn't know myself of-course 😳 )

Strangely a 10 speed cassette is narrower than a 9 speed.

Well it is and it isn't. The bit which fits on the splines is narrower and so needs a spacer. The actual cog bit is very slightly wider (the big cog overhangs the splines). Yes it will fit on a 9-speed hub.

Yes, as above, I did the same with an ultegra cassette last week.