Saft can mean different things. Juice is more like "juice/jos" in Swedish and it typically means juice made from real fruit. Saft is more like syrup or sap (if it comes from plants). "Saften" that you drink is made of sugar with (sometimes artificial) flavors. If you buy a bottle in the store that has the lable "saft" on it, you need to mix it with a lot of water before drinking it, because it is highly concentrated.
I made this mistake the hard way when i tried drinking a bottle of what i later found out was juice concentrate straight out of the bottle. It was my first trip to Sweden and i remember thinking "wow, Swedes sure like their juice sweet here!". I'm ashamed to admit it took me like three or four sips before i realised...
Generally, as you have already stated, "saft" would translate to cordial. It can also mean the juice that comes out of a fruit for example when you squeeze a plum and it starts running. Had a few mistakes in this Swedish one, makes me wonder how accurate Duolingo really is...
Juice is 100 percent juice from fruit/vegetables. In Swedish class we were always taught that saft was cordial, just as explained very well in the first comment here - a concentrate with water added to it. I've always used jos or juice for juice. Though jos wasn't accepted here on Duolingo last time I used it.
In the UK, punch is assumed to be alcoholic (a mixture of spirits, juice, sometimes wine, fruit pieces, often some fizzy soft drink- for example vodka, orange juice, lemonade, and chopped fruit). Non-alcoholic punch is specified as such (usually at a party where children are also present). It's generally served in a big bowl with a ladle, and usually considered a summer drink for having outdoors.
I think the meaning has changed over time, though: "The word punch is a loanword from Hindi. The original drink was named paantsch, which is Hindi for "five", and the drink was made from five different ingredients: spirit, sugar, lemon, water, and tea or spices. The drink was brought back from India to England by the sailors and employees of the British East India Company in the early seventeenth century, and from there it was introduced into other European countries." [Wikipedia- Punch Bowl]
This is the same definition of "punch" we use in the U.S. One small difference is that we probably assume it's non-alcoholic as it's served at all kinds of parties. In certain settings, we would expect it to be alcoholic, but one might have to ask (or taste). One other difference is that it's not necessarily an outdoor drink. It's served at lots of indoor events like dances, church socials, children's birthday parties, piano recitals, graduation parties, formal and informal dances.
Thanks for the history. Very interesting! :D