Do crank arm pullers vary in sizes or there is just one size? Just want to confirm if there are different types of crank arm pullers? I'm trying to order one and the contact person is telling me that he has one but for a road bike. Now I'm confused I thought there is only 1 size of crank arm puller, so are there different sized of crank arm pullers?
The main distinction is whether the puller is for square taper (and Powerspline) versus Octalink/ISIS. Among square taper crank pullers, there are some older ones made with nutted spindles in mind that don't play nice with the now more common bolt-style ones because their tips are too narrow and can jam into the bolt hole and damage the threads. A couple companies now have good all-in-one tools with switchable tips that work on both square taper and Octalink/ISIS. 

There is no road versus mountain distinction with crank pullers.

One size of extractor thread has been used on the vast majority of cranks for a long time, M22x1. There are several older sizes on cranks made by T/A, Stronglight, and possibly some more obscure ones, all of which need their own extractors. There's also some more contemporary brand/model specific designs such as the Profile ones and Cannondale SI.

Within BMX, there's now about a million model-specific crank removal tools, and a whole other discussion of cross-compatibility.