Natural philosophy in the early modern period is roughly what we today would call science

http://www.library.usyd.edu.au/libraries/rare/modernity/natphil.html

Natural philosophy became a science when it became apparent to those who studied natural philosophy, that certain things follow certain rules. Newton is a good example. He noted that things fall not haphazardly but with determinable trajectories.

Now this is somewhat different to philosophy in general where (I think it is best said),

"Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect" - Bertrand Russell

Natural philosophy branches from philosophy in general as it seems to deal in that which is determinable via experiment. This then leads to the development of the scientific method and from here science begins.

A rather small selection of branches and authors can be found in the provided link. There are more to be found.

The Stanford Encyclopedia of Philosophy is helpful and trustworthy. Aristotle's Natural Philosophy (Stanford Encyclopedia of Philosophy)