"Mahjong" is sort of like the card game "rummy"; both have 2, 3, and 4 player versions. The 2 player arcade mahjong is more like "gin rummy".
Except there are way more variations of mahjong. "Chinese Classic Mah-Jongg", "Hong Kong Mahjong", "Taiwanese Mahjong", "Japanese Mahjong", and "Vanilla Westen Mahjong" are some examples of 4 player variations; most of the differences is in the scoring and what makes a winning hand, but even each of these have varying "house rules", some what like "poker".
The "mahjong" you see a lot as PC games are like saying "I'm going to play baseball," going outside with a plastic bat, swinging the bat and running in a square, all by yourself. You can play solitare with poker cards, you sure don't call it poker. The PC games are called "solitaire mahjong", "Shanhai Mahjong", or "tile matching". "Tile matching" is the most accurate name, but that has no marketing appeal, so marketing has abused a word ("Mahjong") so much it is starting to take up a new meaning, again.
Personally, I have been playing what I believe is a "chinese classical mahjong, with some hong kong rules, and simplified scoring" with physical tiles with some of my friends. I few people I know (and played with) play Hong Kong with the real scoring. I like them more than the 2 player mame mahjongs I've tested, but I havn't tried very many.
A couple other mahjong links:
Mah-Jongg FAQ mostly real mahjong, but includes refs to mahjong in mame.
links to rulessimple classic rules