What's the difference between SMTP server and SMTP Relay?
If I want to send mail from a forum (XenForo) using Google SMTP (Paid Google Apps account), do I need to use Google SMTP server or Google SMTP relay service?
Their functions are mainly the same, but the subtle differences are based on where they are located in the mailchain, hence they support sligtly different usages.
SMTP Server is somewhat generic and can mean any server utilizing the SMTP protocol. However, in this context, it means the server to which a mail client (for example Thunderbird) connects to to send the mail. In additionally to being the first point through which the mail passes, it is also usually the last, as SMTP servers are responsible for delivering the mail to a mailbox (POP3 or IMAP, usually).
SMTP Relay is a more specific term. Think of it like a post office sorting facility - It deals with mail coming from other servers, such as the SMTP server above. It then passes it on in the right direction to other SMTP servers.
To simply be able to send the mail, you do not need a relay server. Additionally, it is recommended to not allow relaying unless you really need to, as an SMTP relay can be abused by spammers.