As far as I know, these are the only keys that react when a button has focus.
Pressing Enter instantly \'clicks\' the button, even if you keep it the key dow
You're seeing two different behaviors, which aren't associated except that they both deal with keyboard events on a winform.
Enter is special because it's the keypress to activate the acceptButton of a form. In fact, you missed another key that can affect buttons: Esc is the cancelButton, and will throw events as well.
As PhaDaPhunk explained, Space is a MouseClick
for any component that accepts a MouseClick, but I haven't found a detailed explanation for it. I'd assume it's the default behavior of all controls. The Microsoft guide to accessibility seems to imply that is so in their section on keyboard-based navigation
Incidentally, this Microsoft support knowledge base entry seems to show that the spacebar implementation went from Button.Click to Button.MouseClick. Perhaps that's the reason for it's different behavior.