generally a subwoofer comes with one coil. sometimes its offered in a secondary impedance for more amplifier options. for example, you might be able to get one subwoofer in a 2 ohm or a 4 ohm. Those are different gauge voice coils. One coil is actually thicker than the other, but genearlly only very slightly. The steel gap plate is also compensated for the difference in coil thickness so that the usually the thiele small parameters are very similar for both impedances. Sometimes you'll see dual or even quad voice coils. These are identical to single voice coils except the coil is cut in half and then you have the options of connecting back in series or parallel. The advantage here is that you can connect it back in parallel and reduce the resistance further to draw more current from the amplifier at the same voltage. This of course puts most amplifiers at higher risk because they are producing more power and generating more heat.
If you are talking about different coils for different subwofoers, well I can assure you that you need not worry so much about that. There are literally hundrends of numbers when it comes to designing a voice coil and most of them you'll never need to know. Even more complex is the theory of linear drivers and then understanding how voice coils behave in a 2D non-linear magnetic flux field. Trust me, its not worth getting into unless you plan on designing your own.
One of the many myths about coils is that the better coils take more power. This is really not what you're after. What you're after is SPL and unfortunately there are no voice coils for speakers that can avoid heating up because they generally use metals like aluminum or copper. All too often people consider how many "watts" a driver (subwoofer) can take but rarely plot or calculate the actual response in a system which will tell you much more. For example, there is no point in putting 1000 watts on a driver if you blow past xmax in your passband. Likewise, there is no point in getting a low sensitivity woofer that has very high xmax and then not being able to use it all because you dont have the power.
The major differences between aluminum and copper are mass. Copper has triple the mass of aluminum, but at the same time it cools better and conducts better. So the copper coil will be able to handle more current and provide more BL product for a normalized resistive load. But the mass differences actually make aluminum more ideal is most circumstances therefore most voice coils are aluminum.