Difference between Button with image, ImageButton, and clickable ImageView?

This probably only covers part of the differences, it would be helpful to actually look at the Android Source tree to see exactly what's going on.

ImageButtons has push states, where as a clickable image does not. You also can't call setText for ImageButton, you can with a regular button.

They all derive from view, but looking at the following extends chain may help a little.

java.lang.Object
↳ android.view.View
   ↳ android.widget.ImageView
       ↳ android.widget.ImageButton

versus

java.lang.Object
↳ android.view.View
   ↳ android.widget.TextView
       ↳ android.widget.Button

The differences can be subtle. The most direct way to understanding this is to start with looking at the docs. If you look at the docs for Button you can see that Button is derived from TextView. ImageButton on the other hand is derived from ImageView. So fundamentally, a Button can have text and is clickable, whereas an ImageButton is a bit more flexible in how you set the image. It has methods from its ImageView base class like setImageURI which a Button does not. One of the differences between these two and just a plain ImageView is that you can have button states which is explained in both of the Button and ImageButton docs.

ImageView = Display Images (android:src)

ImageButton = Diaplay Images as imageView and get click effect as button (android:src) and cannot set text to it.

Button = set text and (android:background)

One other aspect not mentioned in the previous answers is the usage within (for instance) a list item view. If you an embed a Button or ImageButton, the rest of the list item will not receive touch events. But if you use ImageView, it will.