.cer and .crt files are essentially the same thing: a certificate. The certificates may be encoded as binary DER or as ASCII PEM. DER is a binary encoding that can be converted to PEM encoding by using a base64 encode function and surrounding it with the proper headers.
A .p7b/.p7m file consists of one or more .cer files.
Format of messages sent to a certification authority (CA) to request certification of a public key. Also known as a Certificate Signing Request (CSR). A successful CSR will return a .p7b file.
A .p12/.pfx file stores private keys with the corresponding public key certificate, protected by a password.
Convert a .p7b to PEM (source)
openssl pkcs7 -inform der -in a.p7b -out a.cer
Export certificates from a .p12/.pfx (source)
openssl pkcs12 -in INPUT.p12 -clcerts -nokeys | sed -ne '/-BEGIN CERTIFICATE-/,/-END CERTIFICATE-/p' > OUTPUT.cer
Export private keys from a .p12/.pfx (source)
openssl pkcs12 -in INPUT.p12 -nocerts -nodes | sed -ne '/-BEGIN PRIVATE KEY-/,/-END PRIVATE KEY-/p' > OUTPUT.key