If you read almost any of the most popular shonen manga, you'll probably encounter a certain concept very similar to life energy/force etc. I've seen many people on the internet having questions on how similar are they and their applicability in real life, which isn't any less complicated on its own. Feel free to correct me or add on information even from outside of Anime, because apparently I'm not quite all-knowing about this topic.
Ki (Dragon Ball)
Ki (気 literally "Spirit) is interchangeable with "energy" (エネルギー) in meaning the life force energy or latent energy. It is described by Toriyama as invisible, but can be visible in high concentrations or other ways. Auras of ki radiate from the user when increasing the concentration of it inside their body.
Ki is made up of 3 parts. Genki (元気 lit. "Vigor"), the energy or vital force, Yūki (勇気 lit. "Courage"), the courage, and Shōki (正気 lit. "Mind"), the right-mindedness. When we say "ki", most of the time it refers to Genki, like the Spirit Bomb/Genki Dama (元気玉, lit. "Energy Sphere"), which only one with a pure heart can manipulate or deflect it.
Ki comes from the traditional Chinese concept Qi (氣 or 气), which translates literally to "breath" and figuratively to "material energy", "life force" and "energy flow". It is believed to be a vital force forming part of any living thing, and the central underlying principle in Chinese traditional medicine and in Chinese martial arts.
Chakra originally belonged to God Trees from space. Since being spread by Hagoromo through a practice called ninshū, the pre-weaponised Ninjutsu, chakra has become a form of life energy that all individuals produce to some degree; those who run out of chakra will die. Produced within the "chakra coils" that mainly surround and connect to each chakra-producing organ, the energy circulates throughout the body in a network called the "Chakra Pathway System", which is similar to the cardiovascular system. Certain groups, such as Shinobi, have learned to generate more chakra and release it outside their bodies through pressure points called Chakra Points/Tenketsu (点穴 lit. pressure point) in order to perform Jutsu (術, Literally meaning: skills/techniques).
Chakra is created when two other forms of energy, known collectively as one's "stamina", are moulded together. Physical energy (身体エネルギー, shintai enerugī) is collected from each and every one of the body's cells and can be increased through training, stimulants, and exercise. Spiritual energy (精神エネルギー, seishin enerugī, English TV: Mental Energy) is derived from the mind's consciousness and can be increased through studying, meditation, and experience.
Chakra is originally comes from Indian religions such as Buddism and Hinduism. They are believed to be part of the subtle body, not the physical body, and connected by energy channels called Nadi (lit. tube or pulse).
Haki (One Piece)
Haki (覇気 lit. "Ambition") is a mysterious power that is found in every living being in the world. In simple terms, Haki is an ability to sense spiritual energy (Kenbunshoku), use life force (Busoshoku) and overpower enemies (Haoshoku). Kenbunshoku Haki (見聞色の覇気 Observation Haki), also known as Mantra (心綱 lit. "Mind Rope"), is a form of Haki that allows the user to sense the presence of others, even if they are concealed from view or too far to see naturally. Busoshoku Haki (武装色の覇気 Armament Haki) is a form of Haki that allows the user to use their spirit to create, in essence, an invisible armor around themselves. Haoshoku Haki (覇王色の覇気 Conqueror's Haki) allows the user to exert their willpower over others, and cannot be attained through training.
Haki appears to be similar in principle to common types of Qi (Chi) found in various other anime and manga series; which is based on the concept of "qi" (or "life-force") in Chinese philosophy.
Nen (Hunter x Hunter)
Nen (念 lit. "Sense") can be used to refer to either Aura (オーラ), the life energy produced by all living bodies vital for survival, or Nen Ability, the skills which utilizes or involves this energy. If one were to lose their entire aura, it would be equivalent to using up all the energy keeping them alive, which would be fatal. The pores or points on the body from which aura flows out from are called "Aura Nodes" (精孔).
Nen can be calculated and expressed in numerical values in the following categories: MOP (maximum ōra power): the maximum aura capacity of the body; POP (potential ōra power): the amount of the body's latent aura; and AOP (actual ōra power): the amount of aura that can be emitted.
The Four Fundamentals (四大行) are the most basic elements in using Nen and the first step of Nen training is to learn them. Ten (纏 lit. wrap around), is the technique contains aura, making aura stay around the body. Zetsu (絶 lit. sever, suppress) closes all the aura nodes so that Nen is fully contained within the body. Ren (練 lit. practice) improve the aura formed by using Ten, expands their aura nodes and generates more aura than normal while keeping it from flowing away. Hatsu (発 lit. release) is the technique of freely releasing the aura cultivated by Ren.
Reiryoku (霊力, Spiritual Power) is a power aligned with the spiritual sensitivity and willpower of the user. Reiatsu (霊圧, Spiritual Pressure) is the physical force/pressure that a person’s Reiryoku creates when released. Reiryoku is the amount of energy a being has stored within their body or soul, whereas Reiatsu is the pressure that a person’s Reiryoku exerts. All Shinigami have vents located at their wrists that vent out their Reiatsu. If they are blocked off, then the Shinigami in question will be incinerated by their own Reiatsu from within.
The senses by which one feels and pick up on Reiatsu are known as "Reikaku" (霊覚, Spiritual Sense) or "Reiatsu Chikaku" (霊圧知覚, Spiritual Pressure Perception).
Magic (Fairy Tail)
Magic (魔法) is the physical embodiment of the spirit. When the physical spirit of an organism connects with the spiritual flow of nature, the spirit forms Magic as a product of the connection. To utilize Magic, a Mage must use the Magic Power (魔力), the source of Power for all Mages, in their body.
There are two main classifications of Magic: Caster Magic, which is expelled from the body and Holder Magic, which requires a Mage to use an external source to produce the Magic.
For every concept, they have their own uniqueness and difference in details from others, such as if only humans, or even selected humans, possess it. But generally, the big umbrella term would be Life Energy, which all living things would have. The more life energy one has, the more vitality, or "liveliness" one will have, which does not necessarily only apply to humans, but plants as well. Life energy can be natural or mystical, physical or spiritual, which I guess would be up to the writers to decide.
There are also many other series such as Kung Fu Panda, Nanatsu no Taizai, Avatar: the Last Airbender, Black Clover and more which I will leave to more well-informed people. Other interpretations that you can also check out will include Prana, Mana, Ether, Aether, Akasha and more.