Usually, by default, stop loss orders are “stop market” orders, meaning that once they hit the stop price you set, the stop loss order is set as a market order. However, it is possible in some cases depending on the broker, to edit the stop loss order and changing it to other order types.
The trailing stop loss order is very common and it consists of a stop loss order that it moves together with the stock price, trailing at a certain distance that can be specified either as a percentage or as a dollar amount. If the stock price moves away from the stop loss (i.e. goes in the expected direction) the stop loss moves up following the price. If instead the price goes down towards the stop loss, the trailing stop loss remains fixed ad it works as a normal stop market order.