Jet lag is caused by jets, more or less. It is the effect of traveling so fast that your internal, biological clock significantly diverges from solar time, or, in modern society, time zones (which are a modern invention that were created after coordinating shared track for railroads made regionally synchronized time very important — time zones are not "real," they are entirely a product of utility). (Local time, prior to time zones, was reckoned by saying that noon was the peak position of the Sun — this is "solar time," and was standard for millennia.)

Traveling by foot, horse, or boat will not induce jet lag. You need to be traveling very fast for this to occur. (This webpage says it needs to be in the neighborhood of several hundred miles per hour, but it depends on exactly what lines of latitude you are flying — obviously flying straight north/south will not introduce jet lag as an issue.)

Hence the amazement in the 1960s of this essentially new phenomena and the coining of the term.

The most interesting traveling-time-different effects that did occur before jets (in the early modern period, not the ancient ones) that I know of is that of the "missing day" that happens when you cross the equator going westward. This was definitely noted by Magellan's crew when they circumnavigated the globe, because their internal calendar (in the ship's log) ended up off a day from the calendar used at a port they called into:

“On Wednesday, the ninth of July [1522], we arrived at one these islands named Santiago, where we immediately sent the boat ashore to obtain provisions. [...] And we charged our men in the boat that, when they were ashore, they should ask what day it was. They were answered that to the Portuguese it was Thursday, at which they were much amazed, for to us it was Wednesday, and we knew not how we had fallen into error. For every day I, being always in health, had written down each day without any intermission. But, as we were told since, there had been no mistake, for we had always made our voyage westward and had returned to the same place of departure as the sun, wherefore the long voyage had brought the gain of twenty-four hours, as is clearly seen.”

There are some other interesting historical quotes about this kind of experience here. The math of this is pretty straightforward, if you know the Earth is a sphere (which they did) and you know how to calculate solar noon (which they did), but it was apparently unanticipated (because circumnavigation was not a thing prior to this), and even today it is a bit surreal (as anyone who has crossed the international date line can attest).