Let me preface this by saying I am a novice at plumbing. I am replacing a bathroom faucet since the old one was leaking and instead of replacing the guts inside the faucet we decided to replace the whole faucet to something nicer. I also replaced the drain and the drain lift since it came with my new faucet.
I didn't notice until I got the old faucet and drain out and put the new faucet and drain in that the new drain is made out of all plastic which are different dimensions than the copper piping that I had removed from the old drain. So right now, I have the new faucet in and all connected to the water supply, however I am not sure how to connect the black sink drain to the white pvc trap coming out of the wall.
The black sink drain is smooth and not threaded. It is 1 inch in diameter on the inside and about 1.25 inches on the outside of the pipe. For the white PVC trap pipe, the outside diameter of the threading is about 1.9 inches and the inner diameter of it is about 1.5 inches and the black drain pipe is about 4 inches away from the white pvc trap. I am looking for advice on how to connect the black drain pipe to the white pvc pipe. Below are pictures of the issue.