The body is standard base64 (not base64url) of the DER bytes, conventionally in 64-character lines. RFC 7468 labels include CERTIFICATE, X509 CRL, CERTIFICATE REQUEST, PKCS7, CMS, PRIVATE KEY (PKCS #8), ENCRYPTED PRIVATE KEY and PUBLIC KEY (SPKI). OpenSSL's traditional formats add RSA PRIVATE KEY, EC PRIVATE KEY and RSA PUBLIC KEY, and old encrypted keys carry Proc-Type: 4,ENCRYPTED and DEK-Info headers inherited from 1993 Privacy-Enhanced Mail.
A PEM file can hold several objects: a certificate chain (leaf first) or a key followed by its certificate. Text before or between blocks is allowed, which is how openssl x509 -text output can sit next to the base64.
Common errors come from the label, not the base64: no start line (wrong label or a DER file passed as PEM), expecting: ANY PRIVATE KEY (a public key where a private key was expected), CRLF or whitespace damage, and a missing final newline in strict parsers. Converting is lossless: openssl x509 -outform DER and back.