Historically, bloodletting and bloodshed have meant very different things, but over time, the line between them has blurred.
“Bloodshed” refers, quite straightforwardly, to the spilling of another person’s blood — often in the sense of murder or slaughter.
“Bloodletting" dates back to Old English and originally described the ancient practice of extracting blood for what people believed were therapeutic purposes. People once believed that some diseases were caused by an excess of blood which had to be extracted in order to restore balance. This practice continued for many centuries, but thankfully has fallen out of favor.
By the mid-1600s, the Oxford English Dictionary records another meaning for bloodletting: "The shedding of blood or violent, aggressive action, especially killing." The OED also notes that originally, "bloodletting" was used to describe violent action that could serve a good purpose.
Here's an example from 1915 that references India and Burma: "Some bloodletting will become necessary for the health of the body politic." One may not agree with this statement, but it's clear that in the end, the violent killing, the bloodletting, is supposed to be beneficial.
By the second half of the 20th century, it's not clear that the violent killing will always be beneficial. It may just be violent killing, as in this example from 1982: "Rightists and leftists took to the countryside and engaged in a bloodletting unparalleled in the history of modern Turkey." In 2015, President Barack Obama made this comment while discussing Syria: "I think that [Bashar Al-Assad] is going to have to leave in order for the country to stop the bloodletting."
Merriam-Webster still lists both meanings in its online dictionary — the original medicinal sense of bloodletting and the modern sense synonymous with bloodshed. This shows how bloodletting has shifted from a term for healing to one for harm.
There are other meanings throughout the centuries. By the 1700s, "bloodletting" could also be used figuratively to refer to a dramatic reduction or the draining of resources such as money or employees. For example, a company might perform a bloodletting via layoffs.
For more on the various meanings of "bloodletting" and our discussion of the power words hold, listen to the audio above.