The context for the 13th amendment was that slavery was legal in the US then. It mostly wasn’t in other countries, so they never had to try to find the language to allow judicial punishments while disallowing private slavery. If you are given a community service orders without labelling in the UK for example, nobody thinks it’s slavery or servitude, they just think it’s a valid sentence under the law. The grey area is probably around profiting off such work?

> It [slavery] mostly wasn't [legal] in other countries [at the time the 13th Amendment was passed, i.e. the mid 1860's]...

The history of the 19th century and when slavery was abolished in each one is actually a fascinatingly complex subject, and there's tons of interesting history hiding behind your word "mostly", to the point where I can't actually tell whether "mostly" is a correct or incorrect description. Judging by https://en.wikipedia.org/wiki/Timeline_of_abolition_of_slave... I would lean towards "definitely correct in Europe and the Americas, a lot murkier in Africa and Asia". Oddly enough, a lot of Spanish colonies in South America abolished slavery before the United States did, yet Spain itself didn't pass its law ending slavery until a year after the US's 13th Amendment came into effect.

If you're at all interested in the history of that era, the film Amazing Grace, though it takes a few liberties with the historical facts, is a mostly-accurate depiction of what it took to get slavery abolished in the United Kingdom. Interestingly, the part of Prime Minister William Pitt was played by a then-unknown Benedict Cumberbatch (Amazing Grace came out in 2006, and most people first discovered Cumberbatch when Sherlock came out in 2010). I recommend the film if you enjoy historical films; it's quite fun. (I love the "I would have been bored by botany" line).