TIF vs DNG

Personally, TIF has a larger adoption and it's legacy was as a standard before Adobe acquired it. I don't feel DNG has had as strong an adoption as  Adobe had wished.

Or in other words:

raw file > DNG

RGB file > TIFF

TIFF and DNG are cousins, both owned and controlled by Adobe, both openly documented. But DNG is really more useful for containing raw data.

If you wish to render a raw and export it, best to use TIFF. More products support it and you're not embedding raw data. If you're importing raw data, then DNG has a place here and there are some advantages to doing this. So in a nutshell: Data in use DNG. Data out, use TIFF.

Quote

"I recently made some export between Lightroom and another app. Then I have the option to export back the result within Lightroom.

The options are using TIF or DNG..."

I expect that you are using the option in Lightroom Classic to "edit in" a third party application so you will have the following options,

After you finish your further editing in the third party application you are offered the option to save as TIFF or DNG?

So if you sent a tiff from Lightroom and select to save as a tiff, the file will be updated, if you select save as a DNG you will get tiff data in a DNG wrapper. Now you have a tiff sent from Lightroom and a DNG containing tiff data with your edits from the third party application.

Sorry if I did not fully understand the question.

IMO Export to 16bit TIF then you have the full uncompressed file.

Exporting to DNG does not compress the (RGB) file, in fact it might get bigger. You end up with the TIF inside a DNG 'wrapper'.

There are many varieties of DNG. The most common is a DNG converted from a RAW proprietary file- producing the (slightly smaller) DNG 'raw' file.

Other Apps may only 'save' the image file in a DNG wrapper and call it a "DNG".

Camera raw, DNG : Digital Negative (DNG) | Adobe Photoshop CC