If your Theme Editor looks completely different, you're not alone. All Shopify stores, regardless of which theme they are using will have a whole new experience when editing their store.
Here are a few tips on where to find things inside the new editor.
Content blocks like product tabs are now nested within a section, in this case you'll find them under Product page:
To add a new tab, choose Add block:
Hide a tab:
The main product page settings are found by clicking on Product page. If you have a wider browser, the settings will appear on the right side of your browser:
How to modify header content blocks - Menu items:
Tag filter groups can be found when you expand Collection page:
Pages are new grouped by the page template you've chosen: