GENERAL
Souls (魂魄, Konpaku) refers to the spiritual beings that reside in the Rukongai area of Soul Society and the spirits of dead Humans in the World of the Living. While many Souls are deceased Humans from the Human World, it is known that they can be born within Soul Society as well.
Plus
Pluses (整 (プラス), Purasu; Viz: Wholes) are the benign ghosts in the Human World. They are the spirit of a person who has died. A chain, known as the Chain of Fate, protrudes from the chest and connects the soul to its living body. When this chain is severed, the soul can no longer return to its body and live. The soul can move about freely if the chain is broken, but this also causes the chain to slowly corrode. Normally, pluses are sent to Soul Society by Shinigami in a ritual called Konsō before this corrosion becomes significant. If the Chain of Fate is corroded entirely, the Plus will become a Hollow.
Jibakurei
A Jibakurei (地縛霊, Earth-bound Spirit) is a spirit who is not able to leave the Human World that easily because he or she regrets leaving something behind. For example, if the Soul is bound to a place, he or she will stay at this place and refuse to pass on to Soul Society. A Jibakurei is more vulnerable to a Hollow, as being bound to a certain area prevents them from fleeing as far as a normal Plus. This means that the Hollow would only need to search in a small area to find them. It can take months or even years for a Jibakurei to become a Hollow.
Tsukirei
A Tsukirei (憑き霊, Possessive Spirit) is a spirit very similar to a Jibakurei as it is also unable to leave the Human World because of something he or she regrets leaving behind. The difference is that a Tsukirei, instead of being bound to a place, is bound to a person, with the Chain of Fate being wrapped around said person.
Hollow
All Hollows were once Pluses which have lost their heart and become beings of pure instinct. The longer a Plus lingers in the Human World, the more its Chain of Fate erodes by growing small mouths that eat away at itself. This process, called Encroachment, is painful and starts out slow, but the final erosion is much more violent and finally the chain is completely gone and a hole opens in their chest where their heart used to be. At this point, the Soul's body disperses into spirit particles and then reforms nearby as a Hollow. The body usually forms first, followed by the mask. The Hollow's lost heart is its mask and their unique appearance as well as its special abilities. There are other ways to force Hollowfication, such as prying open the hole in a Plus' chest by force, as shown by Don Kanonji.
Arrancar
An Arrancar is a Hollow that has removed its mask, thus gaining Shinigami-like powers and taking on a more humanoid form.
Shinigami
Shinigami are spiritual beings that are responsible for regulating the balance of Souls between the Human World and Soul Society. They act by sending Pluses to the Soul Society by Soul Burial and they are also responsible for fighting and purifying Hollows with their Zanpakutō. Some Souls have spiritual power which can enable them to enter the Shin'ō Academy to become Shinigami.
Artificial Souls
Artificial souls are souls designed by Shinigami scientists to separate a Shinigami's spirit from a Gigai, or to evict stubborn spirits from their corpses if necessary. They are contained within pills called Gikongan, which are often referred to as Soul Candy since the Shinigami Women's Association complained that the name was not cute and had it changed.
Blank
A Blank is a soul with no memory that has become lost in the space between the Soul Society and the Human World, called the Valley of Screams.
Togabito
Togabito are souls condemned to eternity in Hell for crimes they committed during their lifetimes. A Togabito is distinguished as a spirit bound in chains, which are near indestructible.