I’m finding it impossible to shop for these because I’ve only ever bought them in thrift stores and don’t know what they’re properly called.
Edit: Not looking for flannel or denim, but lighterweight fabric, something I’d wear under a jacket not instead of one.

I’ll edit the post to clarify, but I’m specifically looking for the lighterweight kind, linen or cotton or something of that weight.
Maybe you’re looking for chambray? Those will have cat-eye buttons instead of pearl snap and no western yoke/front. Denim can be lightweight or heavier too.