Display different menu links based on page/theme
You will need to mange the links in 2 different menus. for example Main Menu for all website links and Blog Menu to have the links related to Blog pages.

Disable the Main Menu and the Secondary Menus from your theme settings.

Now goto blocks pages and configure the main menu block scroll down to bottom

under Show block on specific pages

select All pages except those listed and type blog/*

now save this block configuration and goto configure Blog Menu scroll down to bottom and select Only the listed pages and type the same in texarea ( blog/* ) and save the block configuration.

Now depending on your URL pattern it will display your required menu.