layout of local test copy of my site is totally different from the production si

Hello everyone.
I’m maintaining my wife’s wordpress site.
i’ve decided to make a copy of the site and test it locally on my windows machine using wamp. For that I’ve created a wordpress folder under wamp\www and placed everything there.
I’ve backed up and restored the DB and changed various tables to point the site locally instead of to the production site.
I’ve copied the entire site using ftp.
But when I run it locally – the layout is totally different.
Also the about page shows the wamp page instead of mine.

Could you please help me out understand what’s going on and ways to resolve it?

Thanks a lot for your help,
Ron