A market order says: fill me now, at whatever the best available price is. It executes immediately by matching against existing limit orders on the book, which makes it the right tool when certainty of execution matters more than the exact price.
A limit order says: fill me at this price or better, and wait otherwise. You trade speed for control — the order may sit unfilled indefinitely if the market never reaches your level, but when it does fill, you know the price in advance.
Slippage is what happens when a market order is large relative to what's resting at the best price. If the cheapest available sell orders can't fill your entire buy order, it keeps matching against the next-best prices up the book until it's filled — so the average price you pay ends up worse than the quote you saw a moment earlier.
Beyond these two, most platforms layer on conditional variants — stop-loss, take-profit, and linked orders that cancel or trigger one another — but they're all built from the same two primitives: an unconditional fill now, or a conditional fill at a chosen price.