Should a landing page look different to other pages on a website?

There's been a discussion in my office that landing pages should look exactly like other pages on the site:

• Users will be less confused if pages look the same.

• But landing pages fulfill a specific purpose and should restrict distractions (like menus) while most pages allow for navigation.

• Or is there a happy medium where landing page use certain elements while still focussing on their purpose?

What should landing pages look like?