Being a spiritual person means that you believe in a spiritual reality. This reality affects at the minimum you and your life.
Being spiritually awakened means that the belief you have in the reality of the spiritual world isn’t just a belief. It means that you’ve both witnessed and acknowledged the primacy of the spiritual over the material. There must be a “spiritual awakening” event to have occurred in your life in order to kick off your new life as an awakened being.
Being spiritually enlightened means that you have carried on with a process of spiritual surrender either in this life or a past one. You do not need to be awakened in order to be enlightened or vice versa. Spiritual enlightenment is commonly defined in terms of nonduality which means that one does not perceive a gap between observer and observed. I personally do not think nonduality is sufficient to ascertain enlightenment. But I can understand why this is commonly held.
If someone says they are spiritually awakened and that they believe in spiritual reality, personally, I consider that statement enough. If someone presents themselves as enlightened, though, care must be taken. One must verify that first, they actually understand nonduality. Second, that they must also be capable of the process of surrender. Third, they must be capable of displaying real humility, even if they don’t embody it like Jesus or the Buddha did. Whatever your feelings as to the utility of being humble all the time, you should at least be able to convincingly display it. I’ve seen many who claim to be enlightened who cannot accomplish that simple task. Those are my three criteria, and I would encourage anyone to adopt them as well.
As a final aside I will quote my good friend Paul Follows when he said that “Wisdom can be gained without healing.” If you take nothing else from this answer, I hope you can keep that in mind.