This was the third and final of the original R-Type coin op machines. R-Type was an immensely playable and variable game, mostly due to it's innovative melding of strategy and shoot-em-up concepts into a seamless, playable game. In the original r-type, and the sequel, r-type II, you had to pilot your tiny little ship against multitudes of alien hordes, with only a small pod and numerous weapon power-ups to defend yourself. The genius of the game was the unique nature of the weapons: the pod could be detached and fired into inaccessible area, and the ship itself had the built in ability to fire a large bolt of energy, given enough time to power up.
However, both of these elements have been removed in R-Type LEO.
Presumably, the designers were aiming at a simpler r-type, probably aimed at younger players. Hence, I suspect, it's not called R-Type III. The simplification of the weapons system includes the simplification of the pod system - it works more like a small smart bomb, and can't be intelligently controlled, instead simply seeking the nearest target. In some ways this makes things easier, but it robs the game of it's strategy element. The laser bolt is also notably absent, although a similar principle applies to releasing the pod.
Also, the look is very different. It departed from the moody, gigeresque darkness of the original, into a garish bad-japanese palette of neon greens and pinks. Everything looks like a sweet shop in this version, as opposed to being a frightening slimy alien creature that has to DIE!
It doesn't really feel like an R-Type game, and has been largely ignored by the R-Type faithful, preferring to honour instead the earlier incarnations... Most notably through it's Playstation release a couple of years back, which R-Type LEO was notably absent from.
However, R-Type delta is another story...