301 Redirects On Different Servers

I have to redirect old .htm pages to new .php pages. But this site is also changing hosting companies so it’s on a new server.

Does this mean that all the OLD pages have to be set up on the new server first, in order to be redirected?

The hosting company has recommended a ‘virtual server’ where all the old pages will be set up to redirect to the new pages indefinitely. How is this different to any other server?