How to delete photo from Album and Library at the same time?

Control click on the photo in the album and then click "Delete 1 photo."

You can also first select multiple photos and then control click on one of them and delete all of them.

Or select the image and use command-delete.

Using the menu or using command-delete doesn't actually erase the image-- it is "moved" to Recently Deleted where it will stay for 30 days before disappearing. You can go to Recently Deleted and remove the image completely if you're in a hurry to get rid of it.