Difference between contributed and invited talk
The distinction between contributed and invited talks applies to conferences, and not to departmental seminars.

The details of who asked first, etc, are no reasonable basis for any distinction between seminar talks.

Since getting yourself invited to give a seminar talk tends to be very easy, I would recommend to list them apart from invited conference talks. One can either go for "Invited talks / Contributed talks / Seminar talks" or for "Invited talks / Contributed &amp; Seminar talks" as subcategories.