Annex or extension

[pure one]

What is the difference between an annex and an extension?

[des8]

Not an easy one to define in a few words!
Your local council planning dept has probably guidance on this matter and there is lots online.
One definition of "annex" is: "Accommodation which is ancillary to the main residential dwelling and used for this purpose. It may be interconnecting within the property as a whole (for instance via doorways) or it may be accessed via a completely separate external entrance, but if it forms separate and additional accommodation for the main house, it will be viewed as an annexe."

Extentions are just additions to the property which vary in size and scope from enlarging a single room to building a full two/three story addition

The important difference is the annex is viewed as separate accommodation