A .crt stores the certificate.. in pem format. So a .pem, while it can also have other things like a csr (Certificate signing request), a private key, a public key, or other certs, when it is storing just a cert, is the same thing as a .crt.
A pem is a base 64 encoded file with a header and a footer between each section.
To extract a particular section, a perl script such as the following is totally valid, but feel free to use some of the openssl commands.
perl -ne "\$n++ if /BEGIN/; print if \$n == 1 && /BEGIN/.../END/;" mydomain.pem
where ==1 can be changed to which ever section you need. Obviously if you know exactly the header and footer you require and there is only one of those in the file (usually the case if you keep just the cert and the key in there), you can simplify it:
perl -ne "print if /^-----BEGIN CERTIFICATE-----\$/.../END/;" mydomain.pem