The SMTP server is the send path; SMTP (and ESMTP) are the path outbound messages take.
The POP and IMAP servers are the receive path; the path that you use to download new mail messages.
Your SMTP server configuration — port, SSL or not, user, password — is very likely incorrect.
The settings for most any SMTP servers around are fairly similar, but there are some differences. There's no set list I can provide, though your email provider will generally have a web page with the required settings around.
To verify your settings, use the Connection Doctor (Mail.app > Window > Connection Doctor) to check the current settings.
You'll probably get an error.
Compare your SMTP server settings — not the POP or IMAP settings — with what your provider requires, and to get to the SMTP server settings, select Preferences (Mail.app > Mail > Preferences), select Accounts, select the problematic email account, then select the outgoing SMTP server pop-up and choose the Edit SMTP Server List from the choices, then select the SMTP server involved, and then evaluate and correct the settings to match those for your particular mail provider.