You cannot say one is the study of this and one is the study of that. You can only say the methods that they use to study their subjects. Both the sciences and philosophy deal with ideas (to different degrees) and mostly science but in many methods of inquiry by philosophers deal with “things”.
In some sciences they use the scientific method rather strictly while some (medicine, psychology) delve deeper into more subjective studies. Their methods are mostly within the field of “empirical studies”. Philosophy uses several methods of inquiry. Probably the two most common are “critical thinking” in Analytical philosophy (Anglo-saxon philosophy and those in continental Europe who follow it) and a variety of post-modernesque methods (a small portion of which is actually somewhat slightly useful) based in France/Germany/Spain/Scandanavia though it has more than a few adherants in Anglo-saxon countries. Their methods are extremely diverse which range from truly free inquiry (which can produce a few things worth reading) to total verbal diarhea that no one can make sense of, mostly starting with folks like Derrida (the French king of bullshit) and Heideger (the german king). Again, not everything they said was useless. But apart from the “critical thinking tools” which are more analytical and rational (anglo saxon) and the “post-modernesque tools” which are more based on huge conceptual frameworks centred around human psychology, meaning, power, human-constructs etc (continental Europe) there are still other methods. Some are experimental bordering on the scientific. Others are pure logic (those who deal with classical and new forms of logic). There are also highly conceptual methods like dealing with artificial intelligence where philosophers are trying to devise new methods of inquiry to solve the many unsolved problems of AI.
Again, it is NOT the object of study that can define a field…but their methods of inquiry. And clearly science and philosophy, in both cases, have several methods of inquiry which are difficult to compartmentalise. They also frequently overlap (the methods within each field) and they frequently study the same thing. There are no short amount of scientist/philosophers like Daniel Dennet and Sam Harris and Raymond Tallis and Douglas Hofstadter (formally) who are all highly influental in atheism, artificial intelligence and are humanist. There are also Scientists who I’d have no problem calling a philosopher even though they don’t have formal training (Richard Dawkins, Carl Segan and Neil Degrace Tyson) who are also all atheists and humanists. There are even scientists who dislike philosophy who have approached a few topics using philosophical methods (Stephen Hawking). They have all written works which either use both methods, or rely heavily on source material that used both kinds of methods of inquiry.
To sum it up = method of inquiry is what distinguishes them.