The default from the last (2015-09-24), and as far as I am aware all previous, Raspbian images is indeed LXDE. This may depend on you running
raspi-config, but both the "Desktop GUI" choices there enable
lightdm, which then uses openbox and lxde. Raspi-config runs on the first boot, but if you exit it prematurely or without making a choice you may or may not actually get a graphical login.
Lightdm is the GUI login, (aka. the DM), a separate application from the DE. On Raspbian 8 (aka. jessie) this is enabled via systemd:
systemctl set-default graphical.target
This target wants a "display-manager.service" that doesn't exist initially but I believe
lightdm.service ends up symlinked as that.
On Raspbian 7 (aka. wheezy) it's determined by enabling
lightdm in runlevel 2:
update-rc.d lightdm enable 2
You can tell which one you are using (7 or 8) from
cat /etc/issue, but the end result is the same. Note you don't have to run the above commands if you used
raspi-config to set the boot mode.
Technically lightdm can offer a choice of DE's to load after you login, based on the contents of
/usr/share/xsessions, but the only one in the Raspbian image is LXDE. There are also configs for lightdm itself and openbox, the WM used by LXDE.
DEs generally require a WM, but many WMs (including openbox) can be run alone, without a DE.
Lightdm's home page explains it's configuration.
LXDE has been around almost a decade and was chosen for use on Raspbian because it requires less resources than the other DEs used as Debian defaults (KDE, GNOME, and XFCE). Like other DEs, it is configurable and hence there are superficial differences in appearance, etc., from one distro to another. Via the home page you can find links to the LXDE forum and the LXDE wiki.
Here's our list of questions tagged
lxde and here's the corresponding list at U&L.