Other than the few manufactures still out there making film, the best you may experience is the slight color saturation one company gives over another. Also, to get any 'special' film you either have to buy (order) in 20 roll bricks or 100 ft' rolls and load your own 35mm cassettes..
At one time, some 35mm movie films WERE loaded into 35mm film cans for shooters but the film had to be returned to the lab offering them for processing because the films did NOT conform to standard 35mm film processing OR chemicals.. I don't even know it any of these companies are still out there anymore..
Of course there are the Infrareds in BW and color slide film.. And there used to be a XR-C (Extended Response - Color) film in slide material, very hard to find now if not imposable (last I saw of it was back in the mid 70's) as well as a very thin based film for photo microscopes with a speed of around 10... Ilford had a near IR BW film (extended response in the red end) called SFX 200, but again, finding someone stocking it may be hard unless you live in a BIG city or a large college town.
Kodak offered special spectral response films that were once used in the science of astro photography and long, LONG exposures. AO-III and names like such were once common but now gone and replaced by CCD's and CMOS chips and special filters allowing far more sensitivity than film(s) ever could.
In the astronomy world there ARE special filters of strange and wonderful "colors" that if used with day light films could give some interesting EFX, but like many things "different", these filters are NOT cheap and finding them in a millimeter diameter size to fit YOUR lens of choice could be tricky at best. Filters that block out the wave length of Mercury Vapor lights or transmit Hydrogen Alpha light and on and on... What could they do with regular photography.. in daylight..?
Some people would bake film in their ovens for short periods of time or gas their film in mixtures of gasses in small home made vacuum tanks to get special EFX from their film.
Shooting indoor film outdoor or outdoor film indoor is one way to acquire a 'cheap' EFX.. Color filters are another way..
Shooting a E-6 slide film and having it developed as a negative in standard C-41 chemicals (made for color negative film) gives really whacked out colors, especially when printed as a 'regular' negative. Trouble is, finding someone to do this now-a-days may be tricky other than a 'pro lab'...
Finding X-Ray film to run thru your camera gives soft, often low density BW images of the world around you. Of course you will NOT get ANY kind of a X-Ray EFX, just soft BW negatives of what your camera saw...
Kodalith, a graphic arts BW film sees in 2 tones only.. Black and White.. No tones of gray in between. If used carefully and with a watchful eye this can give some harsh but curious EFX to rim and side lit objects. You can achieve the same EFX on your computer by turning any image into a BW then go into - Color Count - and reduce the count to two colors.. Not all images look good this way, believe me..
Trouble is, a computer and / or digital camera can give a gazillion more EFX than film ever could and many of these neat older films are either gone, going away or need to be bought in major bulk and hundreds spent getting them. Plus, one can scan film or a print, then "Photo Shop" it a million ways achieving almost any EFX you want. However, true IR and UV acquired images still need the film but the digital cameras can do it so much better and in the long run, cheaper, than film ever could. Almost ANY digital camera can capture IR or UV with the proper filter in place to block "white" light. The built in blocking filter WILL diminish some of the EFX but enuf will get thru to give you a pleasant view. Many cameras can be modified, having their cut off filter removed, but some cameras can be bought from the factory with it off already and some allow you to remove it your self, then replace it again.
Good luck and have fun..
Bob - Tucson