Should the app look the same as the website?

The same brand, not the same layout. An app that reproduces the site screen for screen has thrown away the reason somebody installed it.

Why the answer is what it is

What should differ: navigation at the bottom rather than the top, a home screen built around returning rather than around explaining, and reordering in one step. Colours, type and tone stay identical — those are what make it recognisably yours.

What this looks like in practice

A product page has one job. Everything on it that is not helping somebody decide is in the way.

Consistency beats cleverness. A customer learns your store once, and every screen that behaves differently costs them.

The photograph is usually the product page. Everything else is supporting it.

Where a mobile app comes into it

The same screen designed several ways is the point: a catalogue of four hundred lines needs a different home screen from one of forty.