how to integrate phpbb or smf to my website?

here it is example
https://www.mydefrag.com/forum/
u can visit the whole site and the forum and u never loose the main site to go to the forum site.

i dont want something like virtual box forum that one you are at the forum u cant go back to the site.
https://forums.virtualbox.org/index.php?sid=24e3f470d9b05877a2893b9c1b216fb2

btw: what is the name of wordpress forum plataform? what do they use?