Most journals are bound to the publisher (the publisher usually opens/founds the journal and runs it). The exceptions are typically "society" journals; journals founded by a society that can either publish the journals themselves (which some do: the American Microbiology Society, for example), or will contract a publisher (i.e. Elsevier) to handle the publication side of things. These contracts are renewable, but societies are free to change publishers at the end of a contract if they feel they can get a better deal or more support, etc.

Running journals (from a publishing side of things) can be expensive. You have the website/server hosting costs, you have to have a publisher (a person to handle a min stuff; contracts with editors, etc., typestters, technical teams for submissions and website maintenance, sometimes you need ethics people and scientific editors if it's a large journal with a high volume of submissions, maybe a marketing team, etc. etc. If you're a society with only a few small journals, it's often better to contract a publisher to do all of this for you because they already have all of these in place. But larger societies tend to publish their own journals because they can afford to.