Can't speak for other email clients, but the following is true for gmail and the k-9 email client.
() For gmail, deletion of an email on your droid deletes it on the gmail server. Actually, as someone else noted, it sends it to your "trash" folder. In effect, your Droid gmail client is a (somewhat less functional) version of the gmail internet mail system you (can) use on your computer. If you want the fully functional version you can sign onto gmail through your browser and you'll have the fully functional version.
() K-9 is a separate email client which you may (if you choose) use in addition to or instead of the gmail client. Unlike gmail, it separates emails (rather than grouping them in threads.) If you're used to Outlook (or other email clients) that present a list of emails individually, you may find K-9 easier to use.
K-9 is not "hard linked" to the google mail. You may use it for a variety of email servers. However, I use it (in addition to gmail) to read google mail. And unlike the gmail app on the droid, K-9 provides an option to NOT DELETE the email on the server. It simply downloads email and when you delete it on K-9 it remains on the server (but is never downloaded again.)
I use both gmail and K-9 for the reason noted above. There are times I would rather see indvidual emails than to go through the threaded approach used by google mail. (And vice versa.) However, I prefer to delete email on the server from only one program so I don't inadvertently delete email I want to have easy access to on my phone. (It's the premature Alzheimer's.)
If all that seems too complicated, just choose an email client and stick with it.
Please note that there are all sorts of other combinations of email clients and servers available including "touchdown" which apparently works well with Outlook exchange. Or maybe it's Outlook non-Exchange. I can't recall. (Alzheimer's again.) The various combinations and specific server-related issues make it very difficult to propose general rules that meet everyone's requirements. But some investigation of the "gmail," "email," "K-9" and other email clients will usually result in a satisfactory solution.