Well, Ethernet is one of several technologies that can be used to implement a LAN ... but that's really of academic interest for most people, as essentially all LANs that don't use radio waves instead use Ethernet these days, and you can probably tell the difference between an aerial and a socket fairly easily.
However the rest of your question doesn't appear to make any obvious sense. "Enabling" a "modem" in "BIOS" is not part of any operation that gets you to make an internet connection via broadband, is it??
So, chances are that what one manufacturer chooses to call by the terribly jargon-laden punter-unfriendly but technically useful label "Ethernet" and what another manufacturer chooses to call by the terribly user-friendly and uninformative and useless and technically vacuous label "LAN" are the same thing, but whoever is trying to configure the software doesn't actually know what they're doing.
To start with, is the broadband connection ADSL or Cable? If cable, see Robin Walker's web site; if ADSL then someone else will have to help you.