In the sense I'm thinking of, simulation means modeling the components of a system at a relatively low level — such as all the transistors and connections in a CPU — whereas emulation means replicating the functional behavior of a system.

There seems to be conflicting usage about this.

http://www.fhi.ox.ac.uk/__data/assets/pdf_file/0019/3853/brain-emulation-roadmap-report.pdf

The term emulation originates in computer science, where it denotes mimicking the function of a program or computer hardware by having its low‐level functions simulated by another program. While a simulation mimics the outward results, an emulation mimics the internal causal dynamics (at some suitable level of description). The emulation is regarded as successful if the emulated system produces the same outward behaviour and results as the original (possibly with a speed difference). This is somewhat softer than a strict mathematical definition1. [...]

By analogy with a software emulator, we can say that a brain emulator is software (and possibly dedicated non‐brain hardware) that models the states and functional dynamics of a brain at a relatively fine‐grained level of detail.

In particular, a mind emulation is a brain emulator that is detailed and correct enough to produce the phenomenological effects of a mind.

https://secure.wikimedia.org/wikipedia/en/wiki/Emulation

The word emulation refers to: [...]

The low-level simulation of equipment or phenomena by artificial means, such as by software modeling. Note that simulation may also allow an abstract high-level model.

On the other hand, the top-voted answer at http://stackoverflow.com/questions/1584617/simulator-or-emulator-what-is-the-difference says that

Emulation is the process of mimicking the outwardly observable behavior to match an existing target. The internal state of the emulation mechanism does not have to accurately reflect the internal state of the target which it is emulating.

Simulation, on the other hand, involves modeling the underlying state of the target. The end result of a good simulation is that the simulation model will emulate the target which it is simulating.