pull is what you feel on the end of the lines, it is the sum of a number of component vectors.
lift is one of the component vectors. It is in the direction perpendicular to the top surface of the kite, and proportional to the square of the airspeed. This power-square law is why kites are better than sails, the ability to move the kite about relative to the vehicle means you can increase the kites relative wind, which is amplified by the power law.
Another vector is drag, which is in the direction of the aparent wind (from the kite/line's point of view).
Weight is the third main vector, always towards the ground.
Because kites don't have engines, there is no thrust vector. However, since they are manouverable there is a significant momentum component as well. If you have flown a tube kite past the zenith and stalled it up-wind from yourself in a steady wind, you will know all about the momentum term.
If the lift is less than the sum of drag and weight vectors, the kite won't fly. If it's more, the difference is pull.
That's from a physics point of view. From a kiting point of view the words are used in a neuanced way. A kite that is characterised as having a lot of pull will have a lot of lift, even at low speeds, but also possibly a lot of drag. It might have a thick arfoil and/or a low aspect ration. It will pull hard at low and medium speed, but the top-end speed is limited. As your landspeed increases, the aparent wind becomes more "front on". Put another way, the window changes shape and position. Effectivley, the kite has move closer and closer to the edge of it's window, which reduces the lift (without reducing the drag). Eventually you get to maximum speed where the kite can't fly any further "into the wind". My old PL S-Arc is a good example, it pulls like a tractor when I'm not going too fast, and is very stable.
A "high lift" kite realy means it's "low drag relative to the lift". It can fly closer to the edge of the window. It might feel less "grunty" (pull at low speed) to begin with, but as you go faster it's relatively low drag characteristics means the maximum speed is higher. You can sail "higher into the wind", and it will crank up to higher speeds on a strait course. An extreem example of this kind of kite would be a high-aspect ratio buggy racing kite - fast when used expertly, but perhaps a bit fickle and fiddley to fly because it may have a thinner and flatter airfoil and therefor stall at a lower airspeed.
If you want to think about the complete system, you have to consider drag and lateral resistance on your end of the lines. That's another story.