Fashion simply refers to a style or manner through which things are done. A fashion is a term that is used to refer to a common trend, usually for frivolous living. However, fashion is used the most to refer to a kind of appearance or clothing, which might be a new or old style. Fashion can also be used as a verb to mean "to build," "to make" or "to construct."
On the other side of the coin, style can also be used as a noun or a verb. Style as a noun means a manner or way of doing something, especially in a fashionable way or manner. Style can also refer to a legal or traditional term used in reference to a person who holds a post or title.
For example, you can say; "the style of the royal majesty." For those that are used to agriculture or botany in particular, style to them means the stalk that joins the ovary to the stigma in a pistol of the flower.