I looked up the definition of svänga in SAOB - it does mean to move in an arc. Tinycards isn’t always in sync with this course (and also is a little unreliable with translations I’ve found). svänga seems to have many senses.
I would say in English that “turn” and “swing” are not quite the same, even of a car. It’s quite possible that “turn” is the better translation.
Generally svänga is to 'change direction' but vända is to 'turn back'.
It's also possible to specify u-sväng = 'u turn', but if you don't specify that, svänga won't mean 'turn back', only 'turn to the left or right'.
vända can also be used to 'turn something over', very often we'll add a preposition, like vända på problemet 'turn the problem around'. Also, vända upp och ned på = 'turn upside down'.