Yes, the thank-you page does have some standard text, which would include any download links for digital products. Any custom thank-you page HTML you provide (both on a general basis and on a per-product basis) would be appended to our standard text, all together on a single thank-you page.
The thank-you email and the general and per-product thank-you page custom HTML each have their own range of available substitution variables -- they are all listed and described here:
The [%codes%] variable would indeed display on the thank-you page any Stored Codes or Generated Codes that the buyer purchased, so if you are selling Gift Cert. codes, those would be displayed with that variable.
BTW, you can preview your thank-you page by either creating a dummy product with the File Download setting marked, or just temporarily add the File Download setting to an existing product, then use your Seller Admin > "Send free thank-you email / download link" to send yourself a link email for that product. The "download" link in the message for that product actually goes to your thank-you page, where the final download link would normally be offered, but you can use this method to test/preview your thank-you page without going thru a complete checkout.