These terms don't have any definite meanings, although I guess most people have a qualitative feeling for these classifications.

Theoretical chemistry is traditionally associated with paper and pencil type of research, working out new theories or approximations. However, in modern research new methods nearly always need to be implemented in a computer program in order to test the results/implications. The implementation and testing part may be classified either as modern theoretical chemistry or computational chemistry. Using a computer program to investigate chemical problems, however, would probably be at the heart of computational chemistry. Quantum chemistry may be considered as a subfield where only problems involving quantum aspects are considered, e.g. force field and molecular dynamics are not part of quantum chemistry. I am not sure whether very approximative methods like Huckel theory fit into this catagory.

Rene Fournier has collected some thoughts on these distinctions from CCL. One way of making a distinction is to imagine that the amount of computertime/capacity suddenly increased significantly, say by a factor 1000. This would have very little impact on the theoretical chemist, but make a huge difference for the computational chemist. By this definition there are very few theoretical chemists.

An alternative definition is that the focus of a theoretical chemist is on developing and implementing new methods. Once this has been verified by a few benchmark calculations, he/she moves on to develope/implement another method. The computational chemist, on the other hand, will take an existing method, perhaps modify it slightly, and use it for solving a specific problem, and then use it for solving a whole range of related problems. The focus is thus on solving problems, not on developing new methodologies.

Buyong Ma also has some toughts on the philosophy of computational chemistry.