The difference between a leash and a stroller is simple. In a stroller, you are making it so the child doesn't wear himself out walking, or the child is unable (too young) to walk around so you don't wear yourself out carrying her around everywhere. It's a mode of transportation for children. You strap them in so they don't fall out! The leash is to keep them from running away.
I personally don't like the leashes for everyday use (grocery store, out to eat, places like that). I figure if my dad was able to raise 4 kids, all under the age of 6, (My brothers were runners too...) without the leash, I should be able to handle one kid. I think it's important to teach your children to listen when they are told to stop. Although, I do think they are a GOOD thing for places like airports, amusement parks, or places like that where a split second of lost eye contact can result in a missing child.
I do NOT think leashes are cruel, or that it's treating kids like animals... I just feel like I would rather set boundaries, and enforce them, than have to rely on an outside tool.
On that note, this is just my personal opinion. I feel like it's my business that I choose not to use one. Just like if another parent decides that they want to use one, it's THEIR business. I'm not going to judge a parent based on whether their kid is leashed or not... Think of (sorry, can't remember the name) the woman who posted earlier asking about giving her sister one. She had a traumatizing experience, and the leash gives her peace of mind. Seeing her on the street, I would have no clue that she has had a previous experience. So who am I to judge?