The way I think about it is htmx takes the "full page refresh" user experience & programming model, and expands it to "partial page refresh" and goes from there. It also patches some annoying gaps in html, like forms only being able to GET and POST. Finally, it lets you trigger these requests with things other than clicking a link/submitting a form.

LiveView tries to replicate the architecture of a native app toolkit and slap a network boundary in the middle of it, whereas htmx tries to keep the programming model of Web 1.0 apps while radically expanding the user experience possibilities