XBee is a brand name of Digi International for its embedded RF modules. There are many different XBee families.
XBee shield is an Arduino shield that an XBee can be plugged into. XBees often need a different power supply voltage than the MCU they are connected to, and also signal level shifting; circuitry on the shield takes care of this.
XBee Explorer is the name that Sparkfun Electronics gives its XBee breakout boards. An XBee breakout board is similar to a shield in that it accepts an XBee and may do level shifting and power supply regulation, but has a different form factor, so does not plug directly into an Arduino like a shield, but may be used with a breadboard instead. Several companies make XBee breakout boards.
ZigBee is one protocol that certain XBee families use. (ZigBee products are made by many other manufacturers as well.)
HTH. GIYF.