In traditional usage a tire iron is a lever, usually with slightly spooned tip, made for prying the tire on and off the wheel...for old/specialized uses it might also have a tip for disengaging split rims or locking rings. There are specialized shapes for starting the process of breaking the bead area of tires away from the wheel rim...a job that has become much harder in the last few decades due to rust from salt and steel belted tires that are very hard to move.
In the traditional usage, the thing now called a tire iron by most people, the thing that comes in the trunk with the apare, is properly a lug wrench...sometimes the handle is formed as a lever tool, but that generally has to do with removing hubcaps, not tires from rims, and the thing is quite obviously a wrench in form and function.
I think 99% of the people I know would call their lug wrench a tire iron, that usage has pretty well taken over...
Tire irons (except, as noted above, for bikes) are pretty much gone from most people's lives...modern tires are quite difficult to R&R with one, and of course an aluminum wheel would be pretty well chewed up by the things. This is actually a huge social change...to illustrate, every Ford sold through 1948 came with a tire iron (entirely distinct from its lug wrench!) in the standard toolkit. Ordinary people often knew how to dismount a tire and patch a tube, pretty much as bicyclists do now, and it was not uncommon to dismount a tire using a couple of irons and leaving wheel bolted to car as the support...but tires were bigger rim size/smaller carcass back then and much flexier in bead area, so they were not very hard to remove.
Flat tires as a normal life experience started fading away in the late '60's/early '70's in my experience. Now they are considered a disaster, not something you fix and go with.
