It is a different operating system entirely (depending on your definition of "operating system"), yeah, but they have so much in common due to both being Unix derivatives (with BSD being directly descended from the original Bell Labs Unix and Linux, famously, just being a highly inspired and ambitious clone of a Unix kernel :3) that in a lot of cases no to very little effort is needed to port software that runs on Linux to the BSDs, someone who has the code just needs to push the button

For example, even big projects like KDE or GNOME or Firefox work just fine on BSD. The only reason there aren't more things like games on BSD is cuz vendors don't wanna push the button for whatever reason and/or don't wanna make the small effort to port to BSDs. Also some BSDs like FreeBSD have a Linux compatibility layer that just means Linux software just straight-up runs on FreeBSD too by default lol (some exceptions to this)

In the late 90s and early 2000s there was a big push from the corpo Unix vendors to standardize Unix software interfaces and conventions (look up POSIX if u wanna learn more) so they could be smth more akin to a software cartel rather than competitors whose customers were getting increasingly frustrated with their incompatible bullshit and switching to Linux (which was a lot more in those days and the whole OS industry until it was finally coopted later ofc (contentious point :3))

In the end, Linux and BSD (which, famously, was gonna be the choice of a lot of the free software movement for an OS to base their software on until it was embroiled in a decades-long legal scandal regarding who has the rights to AT&T/Bell Labs Unix code) ended up benefiting a lot from this standardization cuz despite not sharing a lot of code due to software license differences they are constructed rather similarly. Arguably more importantly, they're just in the same cultural tradition of Unix and agree on lots of things :3

Also for some more modern, rly complicated stuff, BSDs have just copypasted Linux code and patched it into their kernels. The most immediate example I can think of is the DRM (Direct Rendering Manager) from Linux which is basically the standard for managing hardware-accelerated graphics in an OS kernel outside of Windows (I have no idea what Windows is doing) and it exists in all the still-maintained BSD kernels that I can think of