If you have an active selection in a document and you select the Crop tool, the Crop tool conveniently appears around the selection. If you reposition the crop, it will deselect the area. Artboards don’t share this behavior.
In addition, if you have a selection and choose Edit > Crop Photoshop will crop your image.
I prefer using the Crop tool as it can hide (instead of delete) cropped pixels as well as other options.