Zen is not Buddhism
Zen can never be Buddhism. Neither can Zen be any other ‘ism’. But there can be Zen in Buddhism. Likewise there can be Zen in any other religion, philosophy or way of life.
The concept of Zen is often used as an abbreviation of Zen Buddhism, and for good reasons. Zen is so important in Zen Buddhism that it almost is synonymous. But still: Zen is Zen, and Buddhism is Buddhism. Just like Zen is Zen and Taoism is Taoism, or Christianity is Christianity. Zen is an awareness of the moment, and basically emptiness of everything else. Zen is a method for training this awareness, for training mindfulness. Zen is focused meditation, nothing else. The moment we fill Zen with anything else, it is no longer Zen.
Zen is an universal way of quieting the mind from what’s disturbing. It is an universal method for training insight and awareness. The reasons for doing Zen can be varied, like enlightment, reaching contact with Tao or God, or just to find balance in life. But in practicing Zen, Zen is only Zen, and nothing else.
I agree that we hardly manage to create the silent emptiness when practicing Zen (or zazen), and that our awareness often is disturbed by other thoughts. These thoughts can be of many qualities, including religious, philosophical or existential character. But this intriguing thoughts are basically not Zen, even though our awareness of these thoughts is part of Zen.
Each time we practice there is nothing but Zen, not Buddhism, Suffism, Christianity or Taoism. The core is Zen, anything else is ad-ons. Happily we are free to add.