Atheist say there is no God (which is a belief because they they don't really know that). Agnostic says they just don't know (which is the correct choice). Spiritual means increasing one's feeling of self awareness while we are here on a search for meaning in our lives. Trying to be spiritual is a noble undertaking.
However we should be careful not to equate spiritual with "soul" because more than likely the is no such thing as a soul.

I like Matt Dillhanty (spelling?) definition. Atheist is a lack of belief in a god as there as never been any proof of the existence of a god.
Agnostic is much the same. The word gnostic means knowledge and agnostic means the lack of knowledge of a god or gods.
Spiritual is harder to define as that is a personal experience. For me it is wonder, awe, joy I feel when I contemplate the Cosmos.

Atheism and agnosticism are pretty straight forward but spirituality is far more ambiguous. I believe I'm spiritual because I can be so emotionally moved by things (real things that is) For example, I can be brought to tears when I hear a choir sing Handel's messiah. I'm certainly not religious but it is an amazing piece of work. The exuberance of standing on a precipice, looking down on the vast valley bellow. The thrill of riding my motorbike far too fast, weaving in out of city traffic. THe awe of looking at the vastness of stars as I reflect on how insignificant I am in comparison to the universe. When I create something beautiful and original, it is like an extension of me. When I connect with someone who is a stranger and we realise we are so like-minded. I believe in the interconnectedness of humans and all living things and that no one should be alone because we need each other to thrive. I see the beauty and the pain and this to me is a spiritual experience.

Theist/Atheist: Those that are convinced or unconvinced in the existence of a God(s)
Agnostic: Those who are uncertain to the existence/nonexistence of a God
(Non)Spiritual: Someone who has some sort of innately spiritual belief such as the existence of a Soul.

You can be one, or all of the above, but you can't be a Theist and an Atheist at the same time, naturally. You can be an Agnostic Theist, someone who is unsure as the the existence of a God but still believes there is despite this uncertainty. An Agnostic Atheist, someone who is unsure to the existence of a God and, usually due to that, does not believe there is one. A Spiritual Agnostic Atheist, someone who fulfills the above criteria but is also convinced to the existence of Angels and Demons, just as an example. This is not a comprehensive list of examples and more variables exist, such as what could be referred to as a Gnostic (not the Christian denomination) someone who is convinced of the existence or at least the possibility or probability of the existence of a God(s).

I agree with 'scrunchy'...labels.

Labels

Atheist - not believing in any god(s)
Agnostic - Uncertain of the existence of a god/higher power
Spiritual - probably leans agnostic but believes in an ethereal soul/aura/energy in living things. Some will include plants and animals aside from humans...some will include humans only

Atheist: does not believe in god(s).

Agnostic: undecided about existence of god(s).

Spiritual: senses a connection to all things living and nonliving.

1. Someone who rejects the claims of the existence of a god or gods because they haven’t met their burden of proof and is eagerly willing to change their mind.

2. Someone who holds the position of “we don’t know whether a god exists or not.”

3. I have no clue. I know atheists/ agnostics that saythey are spiritual. But I don’t get it....like meditation and yoga? I don’t think they actually believe in spirits or souls.

1. Someone who does not believe in gods.
2. Someone who acknowledges that there is no evidence gain knowledge about gods.
3. Someone who is honest enough make up their own beliefs instead of becoming a cherry-picker while still calling themselves a Christian/Muslim/Jewish etc.

1. Atheist - someone who DOES NOT believe in any Supreme Being/Deity/Deities what-so-ever, denies the existence of the same, is a true Free-Thinker.
2. Agnostic - someone who is uncertain as to the existence of any Supreme Being/Deity/Deities thus sits on the fence or is hedging their bets,
3. Spiritualist - a vast amount of differences to quantify here, in my opinion, so let's just take on example; A spiritualist - believes that the 'essence' of the being is somehow released from the corporeal body after death and that it continues on existing as an entity in another form not readily detectable to the living but can interact with the living at will.

Atheist - are sure there is no God

Agnostic - it's not possible to know if there is a God or not

Spiritual - don't necessarily believe in the traditional sense of a God (although some do), but believe in a supernatural energy or essence in humans. An intangible like a soul.

1. Don't believe in god(s) as there is no proof

2. Don't care

3. Don't care

Atheist - Nothing supernatural at all.
Agnostic - Will believe in supernatural beings or "power" if evidence is provided.
Spiritual - A belief in a connection between other people an/or other living things. The connection can be super natural or instinctual. So, if instinctually based belief, even an atheist can be spiritual.

I do not see instincts as "supernatural" but rather are hard wired into (most of) us for better survival, and often use unconscious cues, which may or can appear to be supernatural at times, but can be logically explained once they are understood.

Atheist - Positive that gods and religions are bullshit made up by humans
Agnostic - Not sure if gods and religion are bullshit made up by humans
Spiritual - Leaning that gods and religion are bullshit, but want "something" to be there.

1. believing in zero
2. without knowledge of any
3. believing in something unproven

1. Atheist - Do not believe in any gods whatsoever.

2. Agnostic - Don't know one way or the other.

3. Spiritual - Need some woo to hang onto, but don't want religion.

Intelligence!!!

1 lack of theism
2 lack of absolute knowledge
(Important to remember 1 and 2 are not mutually exclusive. Both apply to most rational people)

3 lack of critical thinking, or a nebulous offramp for religion until you realize you're an agnostic atheist.

1. One who has no beliefs concerning deities.
2. One who sees knowledge of god as unobtainable.
3. Whatever unctuous bullshit one wishes to spout.

1. Atheist Someone who has insufficient evidence to justify the reality of a god or gods
2. Agnostic An Atheist with out the courage of their convictions
3. Spiritual In the context of this discussion a hypocrite

Asked and answered a hundred times on here.
The great thing about words is that they have concrete definitions.
Therefore, it doesn't matter what someone's "personal definition" is because there is, and always will be, a real definition.
Google is your friend if you are looking for definitions.

1. no belief
2. no knowledge
3. no idea

Atheist: I believe there is no supernatural.
Agnostic: Knowing that I can not prove the none existence of something outside of reality, even if I'm sure its bull.
Spiritual: Smoke-screen used by some to hide their belief in things outside of reality.

Atheist: I do not believe there is a god. This can also mean I do not believe in god.

Agnostic: without Knowledge, depending on very loose definitions on can not say that a god that by definition can not be perceived can not exist by definition.

Spiritual: anything and everything. The important thing here is if you say spiritual it will be misunderstood by the person hearing. This is believing that the metaphysical exist. By definition if it does not exist in the physical world it does not exist. the metaphysical is defined as that which exist outside of the physical and thus, by definition does not exist.