Stile
On a window sash’s frame, the stiles are the vertical pieces on the left and from the window pane. Like rails, they’ve grooves for placing the panes inside. Cross muntins extend from stile.
Chris Hill
Like rails, stiles are also used to tag parts in furniture. They mention parts.
Mathews Brothers Company
Cross muntins operate from stile to stile.
Interiors with Attitude, LLC
Stiles are generally considerably wider than muntins and may be thinner than rails.