Here is an overview of all Xenomorph types from the Alien movies, including the facehugger, chestburster, warrior and queen Xenomorphs. As a bonus, I include some better-known Xenomorph types from the games and comic books. I did not include the neomorphs from Alien: Covenant as they are not really a Xenomorph type.
The egg is where the Xenomorph life begins. Featured in all Alien movies (except Prometheus) this leathery orb will cause big trouble if you get too close. Supposedly, it detects movement, vibrations in the ground and even your scent to activate the facehugger inside. Eggs can survive for thousands of years and probably bleed acid if hurt. They come in different sizes and the Aliens can use them as traps in chokepoints.
The next stage in the Xenomorph lifecycle, this crab-like creature will latch on to the nearest host. It doesn't matter if it's a human, an animal, a Predator or even an Engineer. It will wrap its fingers around the victim's face and tail around the neck. They are almost impossible to remove and will kill the victim in the process. It will come off and die after successfully implanting the embryo.
This special facehugger is bigger than the regular one and contains a queen embryo. The queen embryo takes a longer time to hatch than a regular one. In addition, the royal facehugger can contain a Xenomorph warrior embryo designated to protect the Queen. It also has a flipper-like legs and darker skin giving it an aquatic presence.
The chestburster is an infant Xenomorph who is freshly born from a host by biting through the ribcage. It has a small size, no limbs (or very short limbs) and light skin. In a few hours, it will shed its skin and grow rapidly. It is still very aggressive and can attack if provoked. Otherwise, it will try to hide until fully grown.
This is probably the most common Xenomorph type and it is "produced" in large numbers. The warriors can have slightly different appearances, like a domed or ridged head. Lone warriors usually resort to using stealth, but they will attack en masse when there are sufficient numbers available. They use their inner mouths, claws and tail to attack. Often they choose to capture instead of killing their victims.
The queen is one of the biggest Xenomorph types and the leader of the hive. She has a higher intelligence than other members of the hive, although her main purpose is to produce eggs. She does that through her ovipositor. When in need, she will detach from the egg sack and fight for the survival of the hive. Being a female Xenomorph, she has a strong maternal instinct and will do anything to protect her eggs and chestbursters.
The runner is a special type of Xenomorph warrior that is born from a quadruple animal, like a dog or an ox. Through the DNA reflex, it inherits some traits from the host, like it's speed and aggressiveness. It does not have the dorsal tubes on the back like regular warriors and its body is slimmer. The runners also more proficient at walking on walls on ceilings.
The Newborn was a genetic mutation and an offspring of Ripley 8 and the cloned queen born on the Auriga. It killed the queen and considered Ripley 8 to be its mother. It had a very large size from birth and human-like features like light skin and eyes. It almost reached Earth but was eventually killed by Ripley 8. It is undoubtedly one of the ugliest Xenomorph types.
The Predalien is a special type of Xenomorph who is born from a Predator. It has bigger size than a regular Xenomorph warrior and is usually more agressive. It will inherit mandibles and even the dreadlocks from a Predator. Its skin is usually lighter than a regular Xenomorph. The Predalien seen in Aliens vs. Predator: Requiem was also able to impregnate hosts with embryos through its mouth.
The Deacon was not a Xenomorph per se, but more like a close relative of the Xenomorph. It was born from an Engineer who was facehugged with a special type of facehugger on the planet LV-223. It had an inner mouth, an elongated head but no tail. It is unknown if it had acid for blood.
The Praetorian is a royal guard for the queen and her eggs. Although not featured in the movies, it has been present in many Alien vs Predator games as boss type enemy. It is much larger and tougher than a regular warrior but slightly smaller than a queen. It would be great to see the Praetorian in a future Alien movie.
The king Alien also known as the Rogue was a genetic experiment created by Professor Ernst Kleist at Charon Base. It was a creature bigger than all the other Alien types, including the queen. It fought the queen Alien and lost the fight because the queen was able to outsmart it. The Rogue was featured in the Aliens: Rogue comic book and novel, later released as part of the Aliens Omnibus: Volume 3.
Of course, there are many more often ridiculous Xenomorph types in the books and games, but I did not care to mention them in this list. Want to know more about Aliens? Check out the list of the most Badass Aliens.