The article that you follow seems good.
NAT mode means each VM is isolated behind its own router.
NAT Network is the same as NAT except that you can have several VM connected to the same internal router. So, NAT Network networking extends the NAT networking to allow multiple virtual machines to participate...
See ->
https://forums.virtualbox.org/viewtopic.php?f=3&t=69504As for your internet problem , see this one (Changing network address range may help..)->
https://forums.virtualbox.org/viewtopic.php?f=7&t=84665&start=15 (PAGE 2)
and read this one as well ->
https://jekewa.com/blogs/index.php/weBlog/2014/01/09/virtualbox-4-3-adds-nat