Usually, the first thing that comes to mind when we think of phishing is an email that asks you to click on a link. Even though this is still a common way that scammers carry out phishing attacks, they are also getting more creative.
In cases where the scammers aren't asking you to click a link, they most likely want a reply from you. By merely replying to a scammer's email, they will know that your email account is working, and that you actively monitor it. Often, in these instances, the scammers will ask you for something other than your username and password. They may ask you for your personal cell phone number, or will continue to message you in order to carry out a more complicated scam.
You can learn more about some of the different types of phishing techniques here!