It does depend very much on the stain used. Spirit/alcohol based stains have a much lower surface tension than water-based stains so get into all the multitude of smaller cracks that water-based stains don't. The tiny cracks are relatively deep, and even heavy scraping won't touch them. Whereas paint or water-based stains are fairly easy to clean off, and if they won't come off with a rag/swab and your choice of cleaning fluid, then a scrape with a sharp blade should do it.

If it's paint you're using, then don't leave it too long to clean of/scrape off as the longer you leave it, the harder the work it is to scrape off as it cures harder and harder.