The difference between your inbox and your application.
Email Service is where your inbox lives on the cloud. Your domain points to this server and your email is routed there.
Email Client is the local software and device you use to access your inbox. This could be an application on your computer or your phone. The email client lets you push and pull messages through the inbox (email service).
You can mix and match this in different ways.
You could use Google (gsuite or google workspace) for your email service and inbox provider; however you can use a local Outlook software as your email client to access your mail.
This can be applied the other way… Having the O365 email service and outlook.com managing your inbox and then using gmail or another phone application to manage your emails through a different interface.
There can also be rules or forwards set up at either level. Some actions can be taken at a service or product level; others can be set up to trigger when you access the inbox and send/receive.
Please check with your web dev to identify the best structure and flow of your emails and organization messaging.