(NPN or PNP ) and (N-Channel or P-Channel). There are two types because its possible and it makes it easier and/or more efficient. Low-side uses N almost always and high-side uses P almost always. If it's connected to ground or the lowest voltage, it's low side. High would be the highest voltage connected. The controlling pin is going to compare voltage or current from one of the other pins, N compares with low and P with high. Hopefully the highest voltage and ground are stable, making it preferable to compare to. Special exceptions are however everywhere.
BJT or MOSFET, really depends on how current and voltage required. They work quite different ways for the control, making them truly not interchangeable. MOSFET handles lower voltage (<100V) cheaply and considerable more current cheaply ( <30A) Yet again there are plenty of special exceptions. The in-efficiency of a MOSFET will be in on resistance. Some have very little resistance while ON, vary small fraction of an Ohm.
BJT are simpler devices that can handle some form of abuse better, high voltage can kill MOSFETS usually easier. They however can not be put in parallel without some extras (using two or more for higher current requires wasting some power across and added resistance). The in-efficiency of BJT is instead dependent on is "ON" voltage. For many devices the lowest voltage "wasted" will be 0.6 volts. For very low voltages use, this may be a larger waste than a resistive switch would do.
Each are controlled differently however. BJT detects current and MOSFET detects voltage. One control circuit isn't going to match the other. BJT requires control to have a set amount of current available while MOSFET will need to change the voltage. BJT control will only need more than the 0.6 volts but an actual amount of current while MOSFET will need to change the voltage by usually several volts.
Frankly, I'd just copy and paste circuits. There are only a dozen usual ways of hooking up any of these devices with given formulas to pick the other components. Pick a device that will handle the voltage and current required and check the datasheet or appnote for an example. The picture has a IRF502 in it. International Rectifier along with almost every other manufacture try to make it easy to use their parts.