Both techniques are used to read email.
The webmail is a web page accessible through a browser and allows you to read and send email from any Internet-connected device. It does not require the installation of programs or configurations.
The messages remain stored remotely on the provider’s server, so they will always be available when the user accesses them. The storage space for messages and attachments varies depending on the provider.
An email client is a program (such as Microsoft Outlook and Mozilla Thunderbird) that must be installed and configured on a specific device. The mail client accesses the server with the specified data and downloads all the content of the configured mailbox locally.
The server is left empty each time the client connects to the mailbox unless the user specifies that a copy of the messages is kept on the server as well. Old messages can only be read from the device on which the mail client was configured.