To add some things to Dennis's excellent exposition,
Brushless electric motors have many ways to specify what they are, but basically what matters in making power is the active volume of the motor---that's where the copper wires are wound and where the permanent magnets are located. The Scorpion and Axi (and some others) specifiy this size as Dennis mentions. So if you want to go between different brands, trying to compare those dimensions is the most useful. Another detail is that all motors have some inefficiency, and the only way they can shed heat is through the outer shell, so the more power you make, the more you need to dissipate into the air. That's why as your needs go up, the physical motor itself will get bigger (diameter and length). Another item of interest, is that the power making part of the motor is made out of mainly copper and iron, so most comparable motors will have similar weight.
There are similar considerations about the batteries. Currently the battery most of us are using is the Lithium Polymer--it maximizes power vs the weight of any other battery out there. Every plane needs a given amount of energy (power in watts times flight time). So that total energy will set the total weight of the battery--since with some variations, you have a nominal energy/ounce of battery. How you arrange that energy is given by the battery designation. For example, if you start with 6 cells each of 2100mAHr capacity, you can arrange them in in two common configurations---a 6s1p2100 pack (6 cells in series), or as a 3s2p2100 pack (two 3s2100 packs hooked up in parallel). Both configurations carry the exact same amount of energy, just arranged differently.
To use the energy effectively, we will choose the "kV" of our motor to match the battery. Recall that in any case you want to turn a prop at some target rpm. A 6s1p2100 pack will have twice the voltage but half the amperage output of a 3s2p2100 pack. So for the 6s pack, we will chose a motor with half the kV than the one we would choose for the 3s2p pack. It is your choice!
I note these options because I am exactly doing this right now with my Vector--I have a motor with a 1088kV and will use two 3s1p2100 packs hooked up in parallel. If I had the same exact motor but wound to give a 544kV, I would hook up the two packs in series (to make a 6s equivalent). Why not just use a single 3s1p4200 pack (made out of three 4200mAHr cells)? --I could but the one I do have is a very tight fit in the Vector (also I only have one).
So you can see there are a lot of ways to skin the same cat--and that can add to the overall confusion sometimes (I have probably helped here in that regard!).