In EMclient Gmail is "Archive" vs "move to folder All Mail"

Q: in eMclient accessing Gmail, is “archive” equivalent to “move to folder All Mail”?

OK so “archive” on Gmail is roughly equivalent to

(a) removing the label:Inbox

(b) moving the folder All Mail.

is “roughly equivalent” exactly equivalent, especially in the context of eMclient accessing GGmail?

Why I ask?

Like many people, I frequently use “archive” when I’m processing my Inbox.

However, I have frequently found it useful to have Gmail rules that skip Inbox and put the email into a lower priority inbox, e.g. one that I call ,Inbox/,riscv, and another that I call ,Inbox/,Clutter.

(I use the prefix ,-commas as a hack towards controlling the sort order of such pseudo-Inbox folders.)

The way Google works, is that all messages are stored in a single folder - All Mail. They then have labels that display them in virtual folders you see as Inbox, Sent, Inbox/Clutter etc.

When you archive a message, whether in the Gmail webmail interface, or in eM Client, all its labels are removed. That is all that happens. The message is not moved at all, it is still in All Mail, it just doesn’t have any labels.