A resistance mutation stays inside one lineage. Bacteria have another way to pick up resistance genes: horizontal gene transfer (HGT), the movement of genetic material between organisms that are not parent and offspring. Three routes do most of this work in bacteria, and they differ in what DNA they move and how far they reach.
Transformation: the cell becomes competent, a physiological state in which it can take up free DNA from its surroundings, and pulls in a loose fragment lying nearby. If that fragment carries a resistance gene, the marker ends up inside the recipient. Free DNA fragments are small, so transformation usually moves a single gene, and mostly between closely related species.
Conjugation: two bacteria connect through a pilus, a mating bridge that forms between them, and a conjugative plasmid slides from the donor into the recipient. The recipient does not need to be competent, only a suitable mating partner. A plasmid is a large, multi-gene piece of DNA, so one conjugation event can hand over several resistance genes at once, and it reaches distantly related species, even different genera. That combination of capacity and reach is why conjugation spreads resistance so effectively.
Transduction: a bacteriophage (a virus that infects bacteria) accidentally packages a fragment of bacterial DNA, resistance gene included, instead of its own genetic material. When the phage attaches to a new cell and injects its contents, that bacterial DNA enters the new host and the marker appears there. Transduction is limited by which bacteria the phage can infect, but it can move genes that are not carried on plasmids at all.
Line the three routes up side by side and the contrast is clear. Transformation takes in a small fragment and stays within close relatives. Transduction carries a moderate piece of DNA but is confined by the phage's host range. Conjugation moves the largest amount of DNA across the widest span of species, so it stands out as the dominant route and the primary driver of resistance spread.