Yes, they are tuned at the same pitch. And according to this source the strings are usually the same gauge too. This means that the strings will be looser (i.e. have less tension) when tuned to the same pitches. The source linked to above suggests that this contributes to smaller sized violins being hard to tune. I don't play violin, but I have certainly noticed that half and three-quarter size guitars tend not to stay in tune as well as full size instruments, and the strings do feel more loose, particularly for small electric guitars.
The source above also points out that you should use shorter strings intended for smaller violins, rather than cutting full-size strings, as you can on guitar, because violin strings have thread wound around the peg end of the string.
EDIT: following the discussion with the OP below, I thought it would be worth noting that a half-size violin does not have strings half the length of a full-size violin. It is not in fact half the size of a full-size instrument, despite its name, and certainly its scale-length is not half that of a full-size instrument. This page gives the scale lengths (string lengths) for different sizes of violin, and other stringed instruments. For example, it lists a full-size violin scale length of 330mm and half-size scale length of 285mm (not 165mm!) Again, this makes sense to me as a guitarist: a half-size guitar would be about the size of a ukelele if it had half the scale length!