Differences between mail server and mail client
To use a mail service, two things are needed: mail server and mail client. It is increasingly common practice to have the customer replace the client with webmail application, which gives more freedom and sort of independance to the user from a particular physical device.
A mail server is a software that runs on a server (computer machine) and constantly communicates over the Internet. It processes any received email and sends each email to a recipient, designated by the sender.
The mail client is an software application, the program you use to view your messages and manage them. This can be an app on your phone, something you see on a URL through your web browser or a desktop application such as Mozilla Thunderbird or Microsoft Outlook.
The email client checks the mail server for new messages and stores them so you can view them. It provides an interface for reading and writing messages. The client uses the sender (SMTP) mail server to send outgoing messages to the receiving (IMAP or POP) mail server on which the recipient's mail is configured.
Webmail client is a web application that lets you check your messages via a browser, regardless of the device you are using or your physical location.
The mail server and mail client are two different types of software that communicate via standardized mail protocols - SMTP, IMAP or POP.
Most email clients can connect to virtually any mail server seamlessly. Most email clients can connect to multiple mail servers and work with multiple mail accounts at the same time.
This means that if you use, for example, Outlook as an email client on your computer to check your personal mail, you can set up the program to go into your office mail also.