No, web hosting typically does not include email hosting because email and web hosting are two different services. Most of the times, you have to purchase a separate plan to host your emails.
Web hosting stores your website and its files on one or more servers while email hosting stores only email-related data. Email hosting cannot run a website, nor can web hosting run email services.
Interestingly, your hosting provider may host your website and emails on the same physical server. You can also choose separate hosts for each of these services.