Robots are constructs that are built for specific purposes, and follow pre-programmed instructions. While complex programming can sometimes make them seem lifelike, they cannot think on their own.
Androids are robots that imitate life, and in some cases may actually be alive.
Type 1
This type of android is the most robotic of them all, but is normally designed to resemble the creating species. The type 1 androids are equipped with advanced artificial intelligence that give them thought, reason, and especially personality.
[R2-D2 and C-3P0 from Star Wars; Analyzer (IQ-9) from Yamato/Star Blazers]
Type 2
These androids have AIs that are even more advanced than the type 1. Plus deliberate attempts are made for them to look as lifelike as possible, but they still are obviously artificial in appearance.
[Data from ST:TNG, Millennium Man.]
Type 3
It is all but impossible to tell the type 3 apart from a natural being... sometimes the difference can only be seen through an autopsy.
[examples can be seen in Daryl, Blade Runner, and Artimage III]
Borgs are half machine and half organic... but now it seems there is some difference in which way it can go.
Cyborgs
Cyborgs are organic creatures that have been enhanced and/or repaired using mechanical and robotic components and limbs. Some cybernetic upgrades involve altering the brain, and in rare cases can result in a hive mind of lots of networked cyborgs.
[examples include 6 million Dollar Man, Bionic Woman, Darth Vader, Luke in Return of the Jedi, Doctor Who's Cybermen, some of the later Honor Harrington books.]
Bio-CyberneticThis is the reverse of Cyborgs. Machines, Robots, or Androids that have been enhanced with the addition of organic parts or components.
[examples include Beast Wars, the starship Voyager from ST:V, and Daryl]
Evolved
This form of living machine evolved into life over a long period of time, maybe starting out as type 1 androids and developing a level of self awareness and self sufficiency, or beginning as a standard robot who had a fortunate short circuit. Once established these mechanoids continue to improve themselves until they firmly establish themselves as alive.
[Transformers, Go-Bots, Jayce and the Wheeled Warriors, Micronauts(?)]
Transferred
These are robot/mechanical bodies who have had the life essence and experiences of a living person transferred into it.
[Machine People in GE:999, Totchiro becoming the Arcadia in Harlock, and Robotix.]
Power Armor
Power Armors are exoskeletons that have been heavily armored and enhanced to increase the wearers agility and dexterity. Frequently they are also equipped with weapons. The most basic of Power Armor however is unarmed, intended for use in mining or construction or rescue operations. Power Armors can be equipped with any number of special abilities.
[Bubblegum Crisis, Maddox 01, Transformers 2010, MOSPEDA/Robotech]
Mechs
Mechs are giant piloted robots. While originally built as construction vehicles, military or police mechs are super tanks. As a generally guide Mechs are built with a humanoid shape, but Mechs can be built in any configuration.
[Mekton Zeta game, Battletech, Gundam, Macross/Robotech]
Multi Form
Multi-form is a special ability that can be installed into robots, Type 1 androids, Power Armor, or Mechs. It is the ability for the unit to transform from one form to another and operate perfectly in either of the available modes. For example, a Mech could transform from a humanoid shape to an airplane and fly away.
[Robotech, Transformers, Go-Bots, Gundam W]
Merging
This is a variation of Multi-form. It is a special mode the unit can transform into that allows it to combine with one or more other units to form a single more powerful unit.
[Transformers, Voltron]