Switching means making an in-country application to change immigration categories.
Switching to PBS dependant
From 1 Oct 2013, applicants in the UK under a different immigration category may apply for leave to remain as PBS dependants from within the UK, providing they are not here illegally, as visitors, or on temporary admission or temporary release. They will still need to satisfy all other existing requirements (319C(h)
An extension application is a leave to remain application to "extend" stay in the UK under the same immigration category.
One cannot apply for leave to remain (extension) from outside the UK. One can only apply for leave to enter (entry clearance) from outside the UK.
See also Family members