There are some background informations in KML, plot of both are around the same time, and a few characters which are in both, but it should work without reading KML, if you don't want to read it. It's just you know less about the other characters that appear.
The dynamic is very different. Josh truely acts as Chase's bodyguard. Josh is badass, he is really strong for an omega, he is no "pushover" like Yeonwoo ( he actually fights back, when he is fed up) . For Chase it needs some time get used to him, understand whats going on with him. But at the end most, if not all, will say that he is much better than Keith.
Do you need to read Kiss Me, Liar to understand this novel/manhwa? Also is the dynamic different to the couple in Kiss Me, Liar?