We'll talk about movable objects, like an animal. They cannot be acquired with money, by paying for them. They wouldn't belong to the buyer even with a payment unless a kinyan (act of acquisition) was done.
We'll talk about three different kinyanim based on how important they are, based on the preference that they have, and on how strong they are in making the kinyan. Number one would be hagbahah, which is the buyer lifting up the object. Number two is meshicha, drawing the object close to him. And number three is mesirah, which is the seller handing over the item to the buyer. A person should always use the best possible kinyan on the item he's talking about, if possible.
We'll talk about what types of kinyanim work with an animal, depending on what their normal usage is. Mishnah says a large animal, a behemah gasah (large animal), can be acquired by handing it over. If the seller hands over the animal's reins to the buyer, it's now acquired. We're talking about a bigger animal here. It can't be acquired by lifting it up; it would be too heavy to do that. But a small animal like a sheep or a goat can only be acquired by lifting it up. That's the higher-level kinyan, and therefore that is what buys or acquires that animal. That's the kinyan for a small animal. Like we said, a large animal can only be acquired by lifting it up—too difficult to lift up—so therefore it can be acquired even by handing it over.
Chachamim (the Sages) say that a small animal can also be acquired by drawing it near to you, since it's an animal that's difficult sometimes to lift up. Lifting it would be a strange way of acquiring it. Therefore, they say even the lower-level kinyan of Mishnah—pulling it near you—is something that could be done in order to acquire it. You don't have to actually lift it up. According to the opinion here of Chachamim, people normally don't lift up animals. It's not so common to do it, so therefore meshicha would be allowed as well.