Is market order a special kind of limit order: is a buy market order equivalent to a limit order with very high (e.g., 10x trading price) buy price.
It may or it may not be. This is an implementation detail and it actually does vary by exchange.
From a user's perspective, it is not. There is no sensible limit visible and expected.
On the CME, though, it actually is implemented exactly like that - it gets treated as a limit order with a limit way on other other side of the spread and thus it is executed immediately and hunting price.
This sometimes causes confusion, for example here: https://tradingtechnologies.atlassian.net/wiki/spaces/KB/pages/1148829/CME+Stop+Market+Orders+Display+as+Stop+Limit+Orders
where someone asks why a stop market order appears as top limit order. This has one advantage that you can actually avoid totally crazy executions that will then automatically bust because there is no orderly market.
I do algo trading, and in my own backtest simulators (I maintain my own inhouse platform) we go rid of market orders and do exactly this - one less code path, and the result is the same.
A market order means that you are guaranteed for your order to be executed and a trade takes place, what is not guaranteed is what price you buy or sell at.
A limit order is not guaranteed to be executed but is guaranteed, if it does get executed, to trade not higher than your buy price or not lower than your sell price.