Most every email client has it’s own way of implementing what is collectively know as archiving.
This depends on the protocol that the client is using to connect to the server, and the type of client used. If you are using POP3, which can only be used on a desktop client, there is no way to archive to a subfolder on the server. And there are many GMail POP3 users. In a webmail interface, there are no local folders, so archiving has to be done to a subfolder of the server. These are two ways of accessing the same email account, but there is no way to implement archiving the same in both. It is unreasonable to say that there is only one way of archiving.