Tags and lottery is a state by state issue.
Many states don’t require tags at all, just a license. It has to do with deer density, hunter density, and season length.
In most of the Southeastern US a license is purchased over the counter and allows the hunter to take x many deer (in NC it was 6 deer, in other states it was 1 per day).
By the time you get to the Midwest the license still gets you a certain number, but often they are by form of take. (For example, if it is 4 deer, all 4 can be taken by archery, but only 2 could be taken by firearm)
Once out west, with more land but significant lower deer density then the lottery draw for tags comes into play. But even then there are often options for OTC (over the counter direct purchase) tags. A prime mule deer area may have limited mule deer tags, but to check the influx of invasive white tails may allow unlimited OTC tags for that species.
And “glorious” species may have a once in a lifetime draw rule. Bighorn sheep often fit in this category