Here is the fifth Mishnah of the chapter, which discusses the difference between a burning coal and a flame. The Mishnah applies this distinction in three areas of halachah, and underlying all of them is a single question: does the item have enough substance to be considered an object subject to the law?
Coal and flame - three halachos:
"Ha-gacheles k'raglei ha-be'alim, v'shel shalheves b'chol makom" - a coal has the same techum status as its owner, and if the owner is restricted to a certain area, the coal too is restricted to that area. But if a person lights a flame from someone else, the flame is not limited to that person's techum; it may go anywhere, because it does not have enough substance to be bound by a techum.
"Gacheles shel hekdesh mo'alin bah, v'shel shalheves lo neheneen v'lo mo'alin" - one who derives benefit from a coal belonging to hekdesh transgresses the prohibition of me'ilah and must bring a me'ilah offering, since the coal is substantial enough to be owned by hekdesh, and it is therefore subject to the laws of hekdesh. But a flame that comes from something belonging to hekdesh - it is forbidden to derive benefit from it in the first place, and this prohibition is rabbinic, yet there is no me'ilah, because on the Torah level a flame does not have enough substance to be considered the property of hekdesh.
"Ha-motzi gacheles l'reshus ha-rabim" - he is liable for desecrating Shabbos, because a coal has substance. But one who carries out a flame, such as by pushing it until it crossed the threshold from a private domain to a public domain, is exempt, because it has no substance.
A pit belonging to an individual, to the townspeople, and to the immigrants from Bavel:
From here the Mishnah moves to a further aspect of the laws of techum, distinguishing between three types of pits:
"Bor shel yachid - k'raglei ha-yachid" - the water in the pit takes on the status of that individual, and its techum depends on his.
"V'shel anshei osah ha-ir - k'raglei anshei osah ha-ir" - a pit belonging to the townspeople: its water is limited to every place that the people of that town may go. Here we follow the common denominator: to any place that all of those people may go, there the water may be taken.
"Shel olei Bavel - k'raglei ha-memaleh" - a well that is under public ownership, meaning that it stands available to the public for the benefit of travelers on the road. "Olei Bavel" is a designation for those people who came up from Bavel. In this case the techum of the water is determined by the one who draws it, since it has the status of ownerless property: it has no owner, and therefore whoever takes it - his techum is what counts.
On this matter we already discussed in Maseches Eruvin a dispute regarding ownerless objects: do they take on the techum of the person who takes possession of them, or perhaps they have a techum of their own, meaning that the place where they were lying determines their techum and they are limited to it in their own right? Our Mishnah holds that ownerless objects do not have a techum of their own; rather, everything depends on the one who picks them up.
In summary: in this Mishnah we learned the distinction between a coal and a flame in three areas - techum, me'ilah with hekdesh, and carrying out on Shabbos - and its basis is the degree of substance the object has. We also learned about the three types of pits: that of an individual, that of the townspeople, and that of the immigrants from Bavel, and that our Mishnah holds that the techum of ownerless objects is determined by whoever picks them up.