You can use either. I call it weight lifting or weight training. You can also call it resistance exercise.

If your neighbor is using the weight while doing cardio, he/she's incorporating some resistance into that program, but it's hardly weight lifting.

To me, heavy lifting means you're pushing as hard as you can, to failure. I'd just say you've started a weightlifting regime, and leave it at that. YOU know what it is. If the 30-rep neighbor thinks that's weightlifting, well - lets just watch YOUR progress, shall we?