If I use openssl to create a certificate authority (CA) root (e.g. this blog post or this MDN article) and use it to sign a certificate signing request (CSR), is the resulting signed certificate considered "self-signed" by current desktop PC browsers (Firefox, Chrome, IE)?
Does the answer depend on whether or not the CA root certificate is installed as a trusted authority in the relevant certificate manager?
My understanding is that the answer should be "No, and no." but I have a problem and don't know where my understanding is incorrect.
According to Wikipedia,
a self-signed certificate is one signed with its own private key.
That is, its creation does not require the signing of a certificate request by a certificate authority. And thus it does not matter whether or not the CA certificate is trusted on the local machine.
EDIT
According to the RFC 5280, Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile:
CA certificates may be further divided into three classes: cross-certificates, self-issued certificates, and self-signed certificates. Cross-certificates are CA certificates in which the issuer and subject are different entities. Cross-certificates describe a trust relationship between the two CAs. Self-issued certificates are CA certificates in which the issuer and subject are the same entity. Self-issued certificates are generated to support changes in policy or operations. Self-signed certificates are self-issued certificates where the digital signature may be verified by the public key bound into the certificate. Self-signed certificates are used to convey a public key for use to begin certification paths.