If the target for drafts is Other: Drafts on Gmail, in Account Settings, Copies & Folders, where Drafts is under [Gmail], then Drafts appears as a purple icon in the Folder Pane, if it is subscribed. If you select just Drafts on Gmail, a second Drafts folder appears. This second folder is in the Subscribe list at the same level as Inbox (right-click the account in the Folder Pane, Subscribe...).

I recommend unsubscribing the second Drafts (and not selecting it as the target), since the one under [Gmail] is the same as Drafts in the webmail version. You'll have to do a test, but I think that is probably the same drafts folder used on the phone.

I'm a bit unclear on how to proceed. In TB account settings under "Drafts and Templates" the first option is selected. In the box to the right of that is my gmail. address. (Screenshot attached.) If I look at my gmail on the web, I see two Drafts, one which appears to be a folder and one which appears to be a label. (Second screenshot attached.) I'm not sure what the difference is, as I never use the web-based gmail, I use TB. I do not see anything in purple, although the Drafts folder under the web-based email is in bold, while the rest of the folders are not. What is it that I need to change to eliminate one of these Drafts folders?

I have the same folder display in webmail. When I compose a message in webmail then Save and close it, it's stored in the Drafts folder that is between Sent and All Mail. This draft also appears in TB in the Drafts folder that is shown in the first picture in my first reply. If I save a draft in TB, it appears in the webmail Drafts folder. So, to have a single Drafts folder in TB that syncs with the webmail Drafts, subscribe to Drafts as in my 2nd picture and unsubscribe the other Drafts in my 3rd picture. The picture attached to this post shows what you should have in Copies & Folders.

This unnecessary complexity is similar to the sent mail setup: messages sent from TB are automatically copied to Sent Mail, and they appear in webmail in Sent. There is no Sent Mail in webmail, and Sent Items is irrelevant.

Do a test by saving a draft on the phone, then check TB and webmail to see where it's saved.