1. to cause (a liquid, especially blood) to stop flowing.
example: The doctor asked for a clamp to stanch the blood.
2. to cause (a cut, wound, drip, or the like) to stop giving off liquid.
example: “Blood trickles from his nose, and from an awful wound on his torso which he has tried to stanch by knotting his shirt around his ribs.” (“Cyberfate,“ Felicity Savage, Fantasy & Science Fiction, Vol. 89 Issue 3, 1995)
of a liquid, especially blood, to cease to flow.
example: “Came behind him, and touched the border of his garment: and immediately her issue of blood stanched.” (Luke 8:44, King James Version of the Bible)
Metaphorical use of “stanch”:
I’m ostensibly in this remote spot to write, but really I’m running from a whole heap of trouble. My marriage is teetering on the brink. My stepdaughter has brought heartache and chaos into our lives. I have doused myself with Malbec wine to stanch the wounds. (National Geographic Traveler, Simon Worrall, “Whipped Into Shape,” 1996)
Easily confused words:
It is not surprising that “stanch” and “staunch” are easy words to confuse. Consider “stanch.” This verb, which means “to stop the flow or course of something (usually blood),” has two legitimate spellings in dictionaries, “stanch” and “staunch.” It also has two valid pronunciations, one rhyming with “ranch,” the other with “launch.” Now, even when spelled “stanch,” this word can be pronounced to rhyme with “launch.” In the dictionary we add a superscript 1 to the spelling “staunch,” because it is a homograph (word spelled the same as another word) of “staunch .” Staunch  is an adjective meaning “firm, solid, or unwavering,” as in a staunch ship or a staunch supporter of animal rights. Staunch  also has an alternative spelling…stanch .
The best way to distinguish between these words when reading is to consider the context and whether stanch/staunch is used as a verb or as an adjective. When writing, stick to the primary spelling of each word and remember: blood is something you stanch, and loyal friends are staunch. The staunch (think “stout”) ship was launched.
The punchline to all this is that, as it turns out, both words derive from the Middle French word estancher, meaning “to stanch or stop.” The earliest meaning of “staunch” in English was in fact “watertight,” as applied to ships. A staunch ship is, etymologically at least, a stanched one.
To conclude, here is a fine tweet on the stanch/staunch distinction from @econstyleguide:
— Style Guide (@econstyleguide) April 11, 2013
This is a handy mnemonic device, which may be all you need. I would argue, however, that the distinction is not precisely “bogus.” These two derivatives of the same French root have different primary spellings and took different paths to becoming English words. “Staunch” entered English about a century later than”stanch” did.