I'm not really sure what the 4-way emulation in Mame is that you are talking about but I'm sure someone here can chime in on that. But as far as the question of whats the difference between a 4-way and 8-way joystick; Its really because trying to use an 8-way joystick to play certain 4-way games just makes control really hard.
A good example is Donkey Kong, If you're using an 8-way (especially an 8-way like a Happ Comp, which easily hits the diagonals), it can be a bit tough coming off the ladders. If you try to quickly go left or right and you accidentally hit the diagonal, the guy will get hung up and not move.
A proper 4-way will restrict you from hitting the diagonals so you don't get hung up.
Of course most guys wanna play both 4 and 8 way games so you have to deal with that issue and many people deal with it different.
The basic options (as I know them) are:
1) Have a dedicated 4-way joystick along with an 8-way or two.
A lot of guys will use a typical dual 8-way fighter setup and have a dedicated 4-way joystick (maybe wired in parrallel with player 1) elsewhere on the control panel.
2) Use Ultimarc U360s and handle the blocking of diagonals through software mapping for needed games.
Many people now prefer this method. I can't say much about it becuase I never tried it. it seems to me that a lot of people like this setup using octagon restrictors in order to feel all directions.
3) Use a 4-way, 8-way switching stick such as the Mag Stick Plus, Sanwa JLW, Omni2 (GGG), Seimitsu or Zippy.
These sticks allow you to change the restrictor setting by repositioning it depending on what you need. They're not all exactly on the fly though.
I guess there are other ways as well. maybe even using octagon restrictor gates so you can at least feel the directions well.
For my control panel, I went with two sticks, Controller one being a Sanwa Jlw sett to allows be 8-way (round restrictor) and controller 2 has the option of being set to 4-way or 8-way. I will be replacing the current Sanwa with an Omni2 so I can just reach up through the coin door and change it accordeing to the game I wanna play. And I just assign my 4-way game controls to that joystick.
I hope that helps you somewhat. I'd advise that you do some searching here on the forums, for the 4-way, 8-way thing, Theres a lot of info here on that.