How to change a term URI based on content type
My answer is going to use two modules, that are tools, not solutions. You will get the flexibility to do most anything you want with the paths, at the cost of needing to understand how the modules work. I will provide an outline of the required configuration below, there are useful videos here, and I will try to update the answer if you get stuck anywhere specific.


Install and enable the Page Manager, as well as Panels
Go to admin/structure/pages/add, and add a Page, with the path video/%video_term
On the next page, click "Change", and pick "Taxonomy term: ID", then pick ID, or Name, as it suites you.
Pick any layout, and just move on until you can click "Finish" to end the wizard. Now fill your layout with whatever content you wish.
Repeat steps 1-4 for your "photo" page.


Since Drupal doesn't allow you to use a variable at the first level, you can't do /%content_type/%term, so instead we create two pages. Personally, I would opt to do something like /products/%content_type/%term, as a single page will lower your maintenance burden down the road. That however, will require understand "Variants", to accommodate two pages in one. The videos will explain that.