Ah. Well. Grunge refers to an era of very late '80s and 'early 90s music - alternative rock - like Sound Garden, Pearl Jam and Nirvana. AND it all started in Seattle. It was a mixture of punk, heavy metal and probably a few other things. (We are huge grunge music fans so that's why I know a bit about this. We love, love, love Chris Cornell from Sound Garden - and saw him in concert again a few weeks ago).
With the music era came a style of grunge clothing - much like what you described. Along with super model Kate Moss who epitomized the grunge fashion look. Very RATE, "just got out of bed chic", rock 'n roll, distressed, tough, thrown together. Not polished.
I wore my version of grunge back in the '90s. Faded 501s with studded belt and combat boots, open flannel shirt with lace camisole underneath. And of course, I was polished. We have to make these looks our own. Order the item of clothing and make it work for you.
Hope that helps.