if I save emails to em client folders I have created, are the emails that are originally in my inbox is the email removed from the mail server I use and copied or moved to my pc or do my emails always stay on my the mail server service and are never put on my pc storage system if I choose?
That depends on where you created the folders. If they are part of an IMAP or Exchange folder tree, then they are stored on the server. If they are in Local Folders, or part of a POP3 folder tree, then they are stored only on your computer.
You can check by logging in to your email account using the web interface for your email provider. If you can see the folders you created and messages in those folders using the web browser, then they are stored on the server.
That helps. I have saved the emails in folders created under local folders! Thanks for clearing that up!