Shinto is an indigenous religion to Japan. Zen is a particular buddhist "methodology". Shinto was in Japan before Buddhism came there. As with all religions, they blended at some point so it really gets hard to label things. as "Shinto", "Zen", "Budo".
By the way, the Zen Mountain Monastery in New York, has Bill Gleason Sensei teaches there as part of their training methodology. They train the mind, body, and soul which requires you to be well rounded.
Zen mediation in itself, it not complete, and is not all encompassing of Zen.
The end state to all this is happiness, peace, or enlightment. Doesn't matter what you call it or how you get there. If it works for you...do it.