Spam, in my opinion, is communicating un-solicited message by any means of communication. A signature on a forum is different however as when you choose to utilize the services of the community you opt-in to do so (by creating an account). Unless the person has expressly agreed to receive said communications, they are considered to be spam. Here is a quote from spamhaus.
Definition of SPAM:
An electronic message is "spam" if (A) the recipient's personal identity and context are irrelevant because the message is equally applicable to many other potential recipients; AND (B) the recipient has not verifiably granted deliberate, explicit, and still-revocable permission for it to be sent.
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pam is an issue about consent, not content. Whether the Unsolicited Bulk Email ("UBE") message is an advert, a scam, porn, a begging letter or an offer of a free lunch, the content is irrelevant - if the message was sent unsolicited and in bulk then the message is spam.
Spam is not a sub-set of UBE, it is not "UBE that is also a scam or that doesn't contain an unsubscribe link". All email sent unsolicited and in bulk is Spam.
This distinction is important because legislators spend inordinate amounts of time attempting to regulate the content of spam messages, and in doing so come up against free speech issues, without realizing that the spam issue is solely about the delivery method.
Various jurisdictions have implemented legislation to control what they call "spam". One particular example is US S.877 (CAN-SPAM Act 2004). Each law addresses "spam" in different ways, and as a consequence, often has different definitions of what they cover, whether they call it "spam" or not. Spamhaus uses the industry standard definition "Unsolicited Bulk Email" which underlines that "it's not about content, it's about consent". As such, arguments as to whether Unsolicited Bulk Email messages are covered under CAN-SPAM or are compliant with CAN-SPAM, are entirely irrelevant.
Important facts about Unsolicited Bulk Email:
(1) The sending of Unsolicited Bulk Email ("UBE") is banned by all Internet service providers worldwide.
(2) Spamhaus's anti-spam blocklist, the SBL, used by more than 1 Billion Internet users, is based on the internationally-accepted definition of Spam as "Unsolicited Bulk Email". Therefore anyone sending UBE on the Internet, regardless of whether the content is commercial or not, illegal or not, is a sender of spam - and thus a spammer. All senders of UBE need to be fully aware that (A) they are breaking their ISP's Terms of Business contracts and they will lose their Internet accounts and access if they send UBE and (B) they will be placed on the Spamhaus Block List (SBL) if they send UBE.
credits:
http://www.spamhaus.org/consumer/definition/