montessori is actually a type of preschool curriculum, i.e. the way/methods/strategies in which things are taught to the kids.
A kindergarten usually only has a half-day progromme, and your kids have to be toilet-trained before enrollment. The teachers are there to mainly teach, and not to take care of toilet-training etc. So, a kindergarten won't have nap time in its schedule.
A childcare/preschool acts like a nanny for your kid, on top of teaching them stuff. So most will offer half and full-day programmes, they have nap times, shower times, and will help to toilet-train your kids.
So you can have montessori preschools/childcare and montessori kindergartens.
Price range is very wide leh, for preschool , the range is from about $500 to more than $2k a month. Working and non-working mothers get subsidies of $150- $300 for childcare only.
Montessori schools tend to be more expensive because of the learning materials used and because the teachers require specialised training.