If labeling and moving are the same thing why does Google give option to do both? I was previously trying to resolve an issue wherein I couldn't select multiple pages of emails and move them to a different category, and came across a comment that stated that they were equivalent and that labelling would work (although it turns out I am only able to label page-by-page as well). Is it true that these are the same thing? Gmail does mention that the labelled emails have been 'added' to a label. Is the difference that labelling adds the mail to another folder while retaining it in the inbox?
The big difference that I see is that when you "Label" a message, it doesn't remove it from the Inbox. But when you "Move" something, it adds the desired "label" and also removes the "Inbox" label.
The Archive button also removes the Inbox label. So, using the "Move" process is the same as first adding a Label, and then clicking "Archive".
As far as selecting many items, you can do it as long as you can create an appropriate search string. For example, say you search for "mom", and you get a list of emails. You can click the "select all" button to mark ll of the messages on that page:
Now, here's the trick: If there were multiple screens of emails that came up because of your search, you will see the following message near the top of the screen (above the email list):
There you have it :)