Back in the days when science was new, Physics dealt with understanding the fundamental laws of the universe, and it was Chemistry that was making the attempt at understanding the fundamental pieces that the universe was composed of. Both of these fields also grew out of a long standing philosophical tradition that can be traced back to the days of the pre-Socratics, and exemplified by Aristotle. Buuuut... that's going a bit further back than I think is necessary to understand what's different, anymore, about these two sciences, if indeed they ever really were different.
Physics, as a science, really began with Newton. It could be traced back further to Galileo, Kepler, and Ptolemy, but he's the big man that laid out a comprehensive scientific theory. Chemistry, likewise, has a big man on campus -- Dalton. Dalton's atomic theory brought back the idea that the universe is composed, at its smallest level, of indivisible particles called "Atoms", and was proposed around the same time as Newton's theory. Likewise, work done by Boyle, Cavendish, and Lavoisier contributed to Chemistry, but Dalton's the guy who proposed the first scientific theory of the atom. (Though mad props must be given to Cavendish, who isolated Hydrogen, Oxygen and created the "element" water -- of four elements fame -- from two different elements of "Air", thereby disproving the idea that four elements created everything and paving the way for the atomic theory)
Newton's theory can be summed up as such:
1) An object at rest remains at rest. An object in motion will stay in motion
2) Momentum is related to Force directly, and is related to mass inversely (F/m=a, from the previous post, except Newton did propose his law in terms of Momentum, a concept accounting for both the mass of an object, and the movement it's currently undergoing)
3) If two objects interact, the force exerted by object A on object B is equal in magnitude and opposite in direction to the force exerted by object B on object A.
And now, Dalton's Atomic Theory:
1) All matter is made of atoms. Atoms are indivisible and indestructible.
2) All atoms of a given element are identical in mass and properties
3) Compounds are formed by a combination of two or more different kinds of atoms.4) A chemical reaction is a rearrangement of atoms
From these two rough outlines, while both are attempting to deal with fundamental pieces of the universe, it seems that initially Physics dealt with a macro-world: How whole objects interact, how cannonballs fly, how wheels spin. Conversely, Chemistry dealt with a micro-world: Fundamental pieces that make up all things, what is actually happening in the micro world, and understanding what effect that has in the macro world.
How things seem to change. Now its the physicists attempting to delve deep into the universe, and the Chemists sit content at the atomic level. Actually, this history makes sense when you think about the things that inspired these two progenitors of the physical sciences. Newton created calculus to better understand astronomy. Dalton collected weather data on a daily basis for 57 years. Newton watched objects moving far away that he had no hopes of understanding without attempting to understand how all objects move. Dalton watched condensation, evaporation, clouds -- a macro world understood through a micro-world of millions of particles interacting with one another.
It's all the physical universe, but when, say, researching a cell, I haven't broken out the quantum equations to understand how it works. I applied concepts traditionally assigned to the realm of chemistry (and, of course, Biology). But, those ideas are in turn heavily influenced by physics (and math), which itself is heavily influenced by math. At present, we don't have a cohesive enough physics model to build towards understanding all biological science, and if we did, it would match up with the findings of biology. It would just be another way to explain it, and the same would happen in building a physics theory of chemistry. Chemistry knowledge, which may one day be obsolete, would serve as the bridge of knowledge between physics and biology, if such a theory is possible.
So, the question still remains, what's the difference? Size? Well, in a sense, yes: I think size is it, in its own way. Not that physicists don't study classical physics anymore, far from. There are still people researching and applying classical physics for purposes other than engineering. But rather, in the number of particles we each deal with. As a chemist, we deal with "System" models most of the time. The "system" model is a method of understanding something, and it's something you define yourself -- generally, chemists define systems as "What's in the beaker". We talk about the energy of a system. We talk about "How Often" a collision between atoms occurs -- not that we really know how often it occurs, exactly, but we do have a way of quantifying it. Physicists deal with points: Displacement of an object, energy transferred from one object to another, the behavior of a single electron. Even with an object of oddly displaced mass, there is an acknowledgment that many particles are moving: But they use the concept of an imaginary representative particle (called the center of mass) in order to apply point-particle models to the object. This isn't always the case, but I have yet to come across having to deal with systems of billions and billions (may Carl Sagan rest in peace) of particles explained by the characteristics of the fundamental particles in my physics studies.
But then you have the physics of condensed matter, dealing with 10^23 particles, and physical chemistry, dealing with the size of a single nucleus. So, the interplay between the two is muddied even further. Which is better? Neither. What's the difference? No idea. It may be the reason Chemistry is given the definition of "The Study of Change" -- it's hard to distinguish what's really different between the two, when we both deal with the physical world at a basic level, sometimes modeled as single points, sometimes billions of points, sometimes a beaker of chemicals, sometimes a ball of mass. In essence, they're really the same: It's the approach that is different. The chemist's explanation can stop at the point we relate a phenomena to an element or compounds composition of elements. The physicist's explanation stops at the point where they have a general rule that can be applied to anything in the universe. Beyond that -- well, I'm still figuring it out.