Your question could justify a couple of pages of responses, but I'll try to hit a few high points from my personal perspective.
1. Lapidary saws do operate at slower rpms (because they are cutting thicker material this may help control heat buildup).
2. Lapidary saws (slab saws here in particular) come with a vice allowing uniform thickness cuts, allowing you to start it and walk away for 15 min instead of pushing constantly with your hands (and this allows you to go slow, go uniformly, and not bind the blade).
3. Lapidary saws can have designs that allow thinner blades, with less hurling of chips, heating of stone etc.
4. Slab saws allow you to have a cover to control mess (and hence use oil instead of water) with all the heat and antirust advantages.
Mostly its precision, durability, convenience, and focused design.
You can make it with a tile saw, but a slab and trim saw will serve you much better.
The analogy from wood working of comparing a hand saw with a table or radial arm saw comes to mind.