Short answer. There technically isn’t a difference, it’s just the amount. Some people will keep their starter in their fridge all of the time, then pull a little bit from it to make a small amount of leaven (aka active starter) in another jar, instead of feeding their entire starter jar. Many people prefer making a leaven if they don’t want to have an excess of discard. Personally, I like to make a lot of loaves at a time or multiple recipes at a time, so I prefer to feed my starter jar a larger amount of flour and water, so I have usually have 2 cups of active starter at a time (which is technically leaven when it becomes active). So it’s just preference. I was always taught to just feed my starter jar instead of making a leaven, so I prefer to keep it simple.