I'm atheist (specifically; transtheist or apatheist) and spiritual.
However, in my view, everyone is spiritual in some way.
For some folks, their spirituality is religious; for others, it is not.
Here's my definition of spirituality:
A set of neurological processes dealing with value placement, empathy and sympathy through the associative truncation of relative identity, and which has reached a value set capable of being described as reverent to the individual, and from which existential experience and reflection is capable explicitly.
A rock concert can be spiritual, so can skydiving, getting married or divorced, looking through a telescope, accomplishing a major milestone in some pursuit, etc...
Objects can be spiritual as well rather easily. Things handed down paternally or maternally through families are spiritual items, a random rock from a beach can be spiritual due to the token of the time at the beach if that experience was remarkable in a sacred way of some kind, etc...
Spirituality is mostly about reverence and the reflections caused by the interaction with revering the given thing, and humans are capable of doing this with pretty much anything in the world.
Religion, on the other hand, is a very organized set of parameters designed to provoke a specific reverential outlook (ontology) through a tool set of methodologies (or ways of thinking), philosophies, moralities, allegories and narratives that are given a tangible experiential representation through religious practices (which differ between religions: prayers, meditations, worship services/sessions/rituals, sigils, etc...) and representative symbols.
Everyone is spiritual in some manner, but that doesn't mean they are religious.
Allot of people state, "spiritual but not religious", but are actually religious. They are, instead, religiously independent - meaning that they do indeed follow a religious construct, but one they have built themselves and not an instituted and organized religion.
Because of the nature of reverence, and the evocative relationship religion has with it; the term of spirituality is very confused and subjective in its use.
I have listed how I see it in this post, but many others will not recognize this as spirituality, and go on to offer vastly different terms tied to concepts of their reverence.
To me, this makes sense. For the individual, I would not expect things without reverence to be recognized as spiritual, and so if the concepts outlined in a proposition to the identified label do not include concepts with which they have reverential response to, then I cannot expect such individuals to accept this description.
Equally, if individuals hold spirituality to be an equal to religion, then I cannot expect them to see spirituality as an inherently secular independent human expression of reverence and evocation thereof that can be attached to a religious paradigm, but is not required to exist as a human expression and experience.