As to the question, what's the difference between the eMail app and the gMail app on your Droid, the eMail app is there to be configured to whatever email program other than gMail that you're using on your desktop, such as one of the POP server type of emails or Exchange emails or whatever you want.
Depending on how you set that one (the eMail app on your Droid) it won't necessary "sync" with your desktop email. For example, I have an email account through my ISP and I've set it up on my Droid eMail so that only NEW messages coming from the ISP show up ... however, I set it (on the Droid) NOT to download those emails from the ISP's server, so those messages still also show up on my Desktop via the Mozilla Thunderbird email app. On the other hand, I've told Thunderbird (on my Desktop) to download the emails from my ISP's server, so once I've read an email on my desktop it does NOT appear on my Droid.
Setting it this way also means that if I leave the email program open on my Desktop, very few if any emails from the ISP will show up on my Droid. This is because I've set Thunderbird to pull emails from the ISP's server every 10 minutes.
This set-up works for me. It provides me access to any new incoming emails (and the chance to reply to them) that I get while away from my Desktop, while still ensuring that everything is there on my Desktop.
On the other hand, I've set up gMail on my Droid and desktop so everything automatically syncs -- which makes sense, because with Google Mail nothing is downloaded permanently -- it's "cloud" computing -- everything is happening in the "cloud" not on your desktop or your Droid. I have found this to work flawlessly so far (knock on wood) -- anything that shows up on gMail on my Droid almost instantly also shows up on gMail on my desktop and vice versa.
One thing that can be confusing is, you really need to make sure your Google account on your Droid is exactly the same as the Google account for your desktop. Many of us have ended up with multiple Google accounts. I consolidated mine before first powering up my Droid, and it's made my life a lot easier.
Finally, I've found you can get pretty useful help on the Google Mail forums -- including help on syncing.