Religion puts the emphasis on tradition, rules, structure, external authority. Spirituality puts the emphasis on individuality, modernity, personal freedom. What they hide with these terms is the opposite side. Religion exists as long as there are people who find their spirituality in it. Spirituality exists because there are other people telling what that means. We usually don't invent our own beliefs, only pick and choose from what we learn about. And we don't believe everything we are told, but only those that feel true to us. Religion gives the illusion of an ultimate truth above us. Spirituality gives the illusion of our freedom from being influenced by others.
Those who prefer religion have the idea of "spiritual people" that they are lost, they are selfish, they are heretics. Those who prefer spirituality think that religion is superficial, militaristic, old fashioned. In the end, both are simple terms for simple thinkers, who find some comfort in identifying with some general idea.
"If the Buddha-Nature is seen, there will be no seeing of a nature in any thing."
(Nirvana Sutra, T12n374p521b3; tr. Yamamoto)
"Neither cultivation nor seated meditation — this is the pure Chan of Tathagata."
(Mazu Daoyi, X1321p3b23; tr. Jinhua Jia)
"With sudden enlightenment to Tathagata Chan,
The six paramitas and myriad means are complete within that essence."
(Yongjia Xuanjue, T2014p395c14; tr. from "The Sword of Wisdom")