what is the difference between a whipping cream and an all purpose cream?

I have never heard of, "all purpose cream". Cream, where I live, is labeled "whipping cream" or "heavy cream" It is used for when a higher fat content is desired. Whether it is labeled whipping or heavy cream makes no difference. Check the back of the carton and it should say 36% milkfat. You can get a light whipping cream which is as low as 30% fat. The higher the fat content, the easier it would be to whip and the more flavor it would have.

The cream used in coffee is, "half & half" which means it is half cream and half milk. and the fat content is about 18%.

Butter fat content. Whipping cream is a higher percentage of butter fat, which is why it is good for whipping. Whip it too long, you will have butter!

Other creams have less butter fat. These creams are good for coffee, and in a lot of forms of cooking, depending on desired outcome. If you over-whip these creams, you'll have some flecks of butter, but not a huge amount.

Read some cream lables and you'll see what I'm talking about.

whipping cream is used to make things like alfredo sauce and for desserts

all purpose cream is for coffee & tea, drinks like white russians