Oh there’s quite a lot of difference. Wax paper is basically tissue paper with a wax coating on the outside, nowhere near as tough and useful as parchment. Parchment is thick (or at any rate thick-er) paper that’s been passed through an acid bath to increase its rigidity and give it a hard, smooth, glossy surface that resists just about everything. Most of the time parchment is also coated with silicone to give it extra stick-resistance.
The result is an all-purpose ktichen paper that stays strong, even when it’s wet or covered with grease, and that won’t melt or catch fire, even in a very hot oven. In short it does everything wax paper can do, only better. It is, how do you say in your country…indispensable.