How to view and delete Mac download history
Yes, macOS does keep a history of everything users download, although users can prevent items from being recorded in that history if they're using their browser's private browsing function or other software designed to ensure your privacy (e.g. the Tor browser, etc).
So, downloading anything in a typical browser (even right-clicking on an image and saving it) is recorded. However, if you're using a private (or incognito)  window (e.g. via shiftcommandN in Safari, Opera or Chrome, or shiftcommandP in Firefox) any items being downloaded will not be recorded in the history.
You can use a terminal command to view what is in your historical record. Note: it’s going to be one extremely long list and you’ll probably find viewing it isn’t very useful. Regardless, you can do this as follows:

Launch Terminal app (usually found in your Utilities folder within the Applications folder)
Once it opens, copy and paste the following command:

sqlite3 ~/Library/Preferences/com.apple.LaunchServices.QuarantineEventsV* 'select LSQuarantineDataURLString from LSQuarantineEvent'

Press return

Terminal will now spit out a long list of addresses pertaining to your downloaded files.
To delete this history, you need to enter (or copy and paste) the following command in Terminal and press return:
sqlite3 ~/Library/Preferences/com.apple.LaunchServices.QuarantineEventsV* 'delete from LSQuarantineEvent'
To confirm that you've deleted your history, just run the first command again.