I'm not familiar with the nuances of terminology, but I would expect MITM to only apply when you (and your computer) actually attempt to connect to service A, and a malicious actor X intercepts that communication. Phishing is different in the sense that you connect to the phishing page directly, and it may or may not replay some of your inputs to the actual service it is phishing.
I guess theoretically phishing could be considered MiTM, but the latter term generally implies the attack is fully transparent to the user, whereas phishing convinces the user to insert the malicious party themselves.
