S.D.
I had these same questions about a year ago. What I found out was that Montessori is a more non-traditional approach to learning. The different age groups are allowed to mingle and I think it's a less structured, more creative/personal discovery approach. Here is the best description I have found: http://www.austinmontessori.org/ I don't know of any other types of schools.
As far as MDO, my 2 1/2 year old daughter is in one right now 2 mornings a week. They go over letters, numbers, sing songs (learning months, days, counting in Spanish), do art projects, and have lots of free play, too. My daughter loves it! Almost every MDO is through a church. The only one I found that is not is Kids Day Out (www.kidsdayout.net). They rent space from a church, but church is not part of the curriculum. They have an optional chapel session once a week, but you can opt out. This is where we go, obviously, and I am very happy with it. I don't think there is another kind of program called Kids Day Out, that's just the name of this program.
In general MDO programs are a few hours a day 2-5 days a week. They are much less expensive than preschool (even part-time preschool).
This is perfect for us. My daughter gets some socialization with other children her age, learns things, and mommy gets a much needed break. I highly recommend it!