I think there is a distinction to be made, but not really as you presented it. Mystical experience does very much include a particular religion's symbols. There are basically different types of mysticism beginning with psychic-level mysticism, to subtle-level mysticism, to causal-level mysticism, to nondual mysticism. The subtle level is very much where encounters with various deity forms arises, visions of Krishna, Jesus, Mary, Kali, Tara, Sophia, etc, etc.
To give you a reference please see the descriptions of these in this explanation of these stages of meditation here paying particular attention to the subtle level: Stages of Meditation | Integral Life
Now as far as distinguishing religious experience from mystical experience, I would say that the experience of religion is most recognizable as a relationship with the external forms; the rituals, the rites, the community, the shared experience, etc. One's identity becomes bound with these forms, and being true to these practices and ways is part of the practice of being faithful and true to one's lineage. Many people never have an internal, mystical experience being part of a religion, but they do benefit from what the externalized forms offer in way of community and belonging, a sense of identity and grounding with culture, etc.
Does this help clarify? BTW, I very much have mystical experiences all the time in meditation that involves deity forms. That is very much a mystical experience, beyond just the religion's teachings. It's direct, immediate, and non-scripted to put a word to it.
So would you insist there is only one legitimate way to categorize mystical and religious experiences?