I'm not sure if there is a concrete answer or not, but I've always though "preschool" to be private/more like daycare as opposed to pre-k which is a literal school enviornment. I believe most people assess pre-k to be more structed learning in an academic setting as opposed to preschool which can still be just fun and games.
Yes, there are both private and public pre-k's. My son was enrolled in pre-k in a public school, but we ended up sending him to a private school. I think with preschool, it's always private--you're paying a location to watch your child.
Preschool will depend on the location, but with public schools depending on your area there is a definite issue! Every year there are reports of children not having seats or being placed outside of their zoned school. It's especially difficult if you are looking for a "full day" pre-k class because most are half-day and few school offer the full day program. It's best to register as early as possible.
I did the application process last year. I'm not sure if the deadline passed or not, but I know you pick your top three choices, and just hope for the best! I know they do everything they can to accomodate as many people as they can and I believe I read they were opening more full day programs/increasing class size.
