As stated, the best thing you can do to understand the differences in the two states is to get a copy of the Hunting Guide. They are available at license agents and most sporting goods stores. Here is a link to the e-version:
http://www.eregulations.com/wp-content/ ... HD-LR3.pdf
Most of the information you are requesting is found in pages 5-8.
Here is the TCA 70-1-101 definition of a resident to determine whether you need resident or nonresident licenses:
(31) "Resident" means any person who resides in this state for a period of ninety (90) consecutive days with the genuine intent of making this state that person's place of permanent abode, and who, when absent, intends to return to this state. For the purposes of this subdivision (a)(31), the following are deemed residents of this state:
(A) Members of the armed services of the United States or any nation allied with the United States, who are on active duty in this state under permanent orders;
(B) Personnel in the diplomatic service of any nation recognized by the United States, who are assigned to duty in this state; and
(C) Students who are attending and have been enrolled at least six (6) months in any school, college, or university in this state
If you are now a resident, you will need the following to deer hunt in TN: Proof of completion of a sanctioned Hunter Education course if born after 1969, a type 01 Hunt/Fish combo, and a big game license that matches up with the weapon you are using (Archery, Muzzleloader, or Firearm). If you use all three weapons during the season, you would need all three big game licenses.
"Permits" are not the same in TN and IL (where I have also hunted for the past 20 years). Your deer "tags" are covered under a license and not a permit. For the statewide deer season, all are purchased over the counter and not through an application process. To a large degree in TN, things that are on a statewide basis are covered by a license. Things that relate to specific areas are covered by a permit.
"Public land" is too broad of a classification to really address your question. Some public land, such as Wildlife Management Area (WMAs )requires a permit, while other public lands do not. Our WMAs that are open with the statewide season usually require a Type 94 permit in addition to the required licenses. Information on all of TN's WMAs is found in the back of the Hunting Guide.
WMAs where the hunting is by a quota process have permits that are issued by a computerized drawing. That drawing has already taken place for the 2019-20 season.
Questions on specific lands is usually best answered by contacting the Regional office in the Region where the land is located.
Hope that helps a little. It isn't as complicated as it seems, but, it is different from IL.