The action of sending emails to fraudulently obtain another person's bank details is called

Phishing sends fraudulent emails to trick people into revealing bank details.

The messages imitate trusted organisations to win the victim's confidence.

Pharming redirects users to fake sites using malicious code.

Spamming is bulk unwanted email without the targeted deception.

Smishing carries the same fraud through text messages instead.

The email channel is what distinguishes phishing here.