What is the difference between a lens with a Sony A mount and a lens with an E mount?
What's the difference?
Although the history of the lenses is quite complex, the difference between the lenses is easy to explain. The A mount lenses are made for Sony's digital SLR cameras and the E mount lenses are made for the mirrorless cameras. In addition, an E mount lens fits both mirrorless cameras with an APS C sensor and mirrorless cameras with a full-frame sensor. The A mount lenses are suitable for only 1 type of image sensor: APS C or full frame.
What type of lens do I need?
If you have a Sony Alpha mirrorless camera, choose an E mount lens. It doesn't matter what type of image sensor you have, the lens fits both a full-frame and an APS C camera. You ultimately base your choice on the quality of the lens. If you're looking for a lens for your Sony SLR camera, then you need an A mount lens. And this lens only fits the type of image sensor of that camera. This is almost always an APS C sensor.
When do I use an adapter?
There are lens mount adapters available that make A mount lenses suitable for Sony E mount cameras. That means you can use an A mount lens on a Sony mirrorless camera with the help of an adapter. This is very useful if you've purchased a new Sony mirrorless camera, but still have several lenses for a Sony SLR camera.