Apple - How do split panes in Terminal work?

It's meant to be like that. See this Super User answer:

You're misinterpreting the feature. It's not meant for two separate terminals. It's intended to allow a user to see two different view points in the same terminal. For instance, if you have 3000 files in a directory, and you perform an ls command, that output is going to be very long.

If you use the split pane, you can scroll through that long output without having to flip back and forth, possibly losing your place along the way.

If you want two terminals, use tabs, or separate windows.

I would add that, for two separate terminals, you can use separate tabs as well.

iTerm 2 supports split panes with independent shells in each pane, not one linked shell.

You should really have a look at screen (that´s an already installed command line tool, not a separate application), which gives you the ability to split your Terminal into two (or more) separate ones. I use that with Visor and it works like a charm. Have a look around here, there are quite a few tips on how to use "screen" on a Mac.