How is X.509 different from PKCS#7 Certificate?

PKCS #7 can be thought of as a format that allows multiple certificates to be bundled together, either DER- or PEM- encoded, and may include certificates and certificate revocation lists (CRLs).
Per RFC2315, PKCS#7 is

• a general syntax for data that may have cryptography applied to it, such as digital signatures and digital envelopes. The syntax admits recursion, so that, for example, one envelope can be nested inside another, or one party can sign some previously enveloped digital data.
  
• More about PKCS#7
  
• PKCS #7 named as “Cryptographic Message Syntax Standard” is one the most famous and extensively used standard from the series of PKCS (Public Key Cryptography Standards) by RSA Security LLC. PKCS #7 is the specific standard used for the generation and verification of digital signatures and certificates managed by a PKI (Public Key Infrastructure). This standard served as the basis for the S/MIME (Secure/Multipurpose Internet Mail Extensions) standard. PKCS #7 proposes a broad-spectrum syntax and format for the creation of digital signatures which is elaborated in detail in RFC 2315. It also allows compatibility with Privacy-Enhanced Mail (PEM) format which is the default and most commonly used file format for storage and sharing of crypto keys and digital certificates. PKCS #7 allows PEM compatible signed-data to be converted into PEM messages.
  
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