In the first state, the horizontal and vertical arrows indicate the firefox has been horizontally and vertically maximized in awesome (respectively). The airplane/other symbol indicates that firefox is floating.
In state 2, the (bolded) plus sign indicates that firefox has been maximized.
When opened, firefox tries to maximize itself. Being maximized and horizontally/vertically maximized are different, but it is very common for configs to only deal with one form or the other.
One way to handle this is to make a shortcut that unmaximizes and unfloats. Something like
clientkeys = awful.util.table.join(
-- among other configuration
awful.key({ modkey, "Shift" }, "m", -- or any command of your choice
function (c)
c.maximized_horizontal = false
c.maximized_vertical = false
c.maximized = false
c.floating = false
end)
)
With this, typing MODKEY+SHIFT+m
will unmaximize the firefox window. Note that various other programs and browsers attempt to both maximize and float themselves as well, and this applies to them too.