Newbie BIND DNS question: resolving upstream hosts?

Old skool UNIX and Linux geek here, but newbie to the world of DNS and bind. I've recently been tasked with replacing our DNS infrastructure, currently on Windows, with a RHEL based solution. And I assume that means using bind, which I've not used before. Here's my question:

Suppose our company name is BigBusiness.com. Our Windows servers running DNS contains a BigBusiness.com zone, with all the names and IP's of our internal servers. Makes sense. But it also contains zones for every external site we connect to as well! So our own DNS server contains zones with name & IP for CompanyB.com CompanyC.com CompanyD.com etc. I don't understand why we need to host and manage zones to look up the IP of other people's equipment?

So I want the end result to be that we've got zones in our DNS for only our own BigBusiness.com machines, and for the lookup of any external machines like www.CompanyB.com, our DNS server looks "upstream" to CompanyB.com's DNS to resolve their names.

Does this make sense? Can Bind do what I'm looking for? And if anyone can share config file examples, it would be much appreciated.

Take a look at: Chapter 4 DNS Configuration Types

So DNS "forwarding" is the feature I should look into?

There's so many DNS buzz-words to learn. Forwarding, Stealth, Recursive, Split, Authoritative, etc.

I thought DNS forwarding would happen automatically? What person would want their companies DNS server to start keeping DNS records for other sites? I know there may be a caching server set up, so that this can occur, but I wouldn't think that the main authoritative DNS server would keep requests that fall outside of its zone.