Do cats snore? Some of us do. Snoring happens when our throat muscles are relaxed while we sleep so they don't move the air through freely. Then the surrounding tissues vibrate making a snoring noise. It also occurs if we have a blocked nose from cat flu. We cats are also more likely to snore if we are overweight or if we have short noses. Sadly humans have bred Persians and other breeds with such snub noses that their upper airways are kind of twisted up. Thus the snore. The really badly affected cats may make a snoring noise when they are awake. Shocking.
It's absurd that humans should laugh at our snoring. Their own snoring is so much louder and unpleasant. I have sometimes had to leave the bed, when my human has a blocked nose and snores horribly.
Purring is completely different. Humans can't do this. The muscles in our throat intermittently close our glottis, the area which includes our vocal chords and the opening between them. Our diaphragm muscles also move and the sound comes out both when we are breathing out, and also when we are breathing in. Some cats purr silently: some loudly.
I purr at medium loudness because it helps my human sleep. And I prefer them to sleep soundly so that they don't wake me up by tossing and turning.