A Jaunt may be described as a short excursion for pleasure or refreshment, but most certainly light-heartedly. It is a ramble, but may also be to prance or frolic.
A Bummel is a journey, long or short, without an end; the only thing regulating it being the necessity of getting back within a given time to the point from which one started. Sometimes it is through busy streets, and sometimes through fields and lanes; sometimes we can be spared for a few hours, and sometimes for a few days. But long or short, but here or there, our thoughts are ever on the running of the sand. We nod and smile to many as we pass; with some we top and talk awhile; and with a few we walk a little way. We have been much interested, and often a little tired. But on the whole we have had a pleasant time, and are sorry when it's over. (JK Jerome, Three Men on the Bummel)