1 - Create a Activity with a Type="ABC" (Controls the Dynamic Layout), save that record and go to the detail page. get the URL
2 - From The report, look at this same Activity and get the URL
Compare both these, they should match for you to see the correct layouts, if not check your Layout Configuration Again.
Also, if your problem is the Layout does not display web-links that are visible on the Edit Layout, you might want to check the Web Link properties and make it available on both Detail and Edit Page , i.e Both