Here is a page that describes theming in PhpBB:
https://www.phpbb.com/styles/create/I am not aware of a good site for hosting PhpBB. For testing, I just downloaded PhpBB on my computer and ran it on an apache server.
I am not sure how the theming is different from tumblr. I didn't notice any differences in capability in the two systems but maybe I do not know enough about them. I also have not looked at the tumblr theme source code because I do not know if it is available online. You can look at the PhpBB theme source code by downloading a theme here and unzipping the folder:
https://www.phpbb.com/customise/db/styles-2PhpBB html templates seem to contain logic in comments, to be processed by some other part of the software. I see lines like
<!-- IF S_DISPLAY_ONLINE_LIST and U_VIEWONLINE -->
in the html template files. I do not know why they do it this way instead of using PHP.