I read the following as meaning "A Pulley is a machine (simple machine), where a Sheave is a part of that machine."
pulley n : a simple machine consisting of a wheel with a groove in which a rope can run to change the direction or point of application of a force applied to the rope [syn: pulley-block, block
Pulley \Pul"ley\, b. t. To raise or lift by means of a pulley. [R.] --Howell.
Pulley \Pul"ley\, n.; pl. Pulleys. [F. poulie, perhaps of Teutonic origin (cf. Poll, v. t.); but cf. OE. poleine, polive, pulley, LL. polanus, and F. poulain, properly, a colt, fr. L. pullus young animal, foal (cf. Pullet, Foal). For the change of sense, cf. F. poutre beam, originally, a filly, and E. easel.] (Mach.) A wheel with a broad rim, or grooved rim, for transmitting power from, or imparting power to, the different parts of machinery, or for changing the direction of motion, by means of a belt, cord, rope, or chain. Note: The pulley, as one of the mechanical powers, consists, in its simplest form, of a grooved wheel, called a sheave, turning within a movable frame or block, by means of a cord or rope attached at one end to a fixed point. The force, acting on the free end of the rope, is thus doubled, but can move the load through only half the space traversed by itself. The rope may also pass over a sheave in another block that is fixed. The end of the rope may be fastened to the movable block, instead of a fixed point, with an additional gain of power, and using either one or two sheaves in the fixed block. Other sheaves may be added, and the power multiplied accordingly. Such an apparatus is called by workmen a block and tackle, or a fall and tackle. See Block. A single fixed pulley gives no increase of power, but serves simply for changing the direction of motion. Band pulley, or Belt pulley, a pulley with a broad face for transmitting power between revolving shafts by means of a belt, or for guiding a belt.
Cone pulley. See Cone pulley. Conical pulley, one of a pair of belt pulleys, each in the shape of a truncated cone, for varying velocities.
Fast pulley, a pulley firmly attached upon a shaft.
Loose pulley, a pulley loose on a shaft, to interrupt the transmission of motion in machinery. See Fast and loose pulleys, under Fast.
Parting pulley, a belt pulley made in semicircular halves, which can be bolted together, to facilitate application to, or removal from, a shaft.
Pulley block. Same as Block, n. 6.
Pulley stile (Arch.), the upright of the window frame into which a pulley is fixed and along which the sash slides. Split pulley, a parting pulley.
Sheave \Sheave\, n. [Akin to OD. schijve orb, disk, wheel, D. schiff, G. scheibe, Icel. sk[=i]fa a shaving, slice; cf. Gr. ??? a staff. Cf. Shift, v., Shive.] A wheel having a groove in the rim for a rope to work in, and set in a block, mast, or the like; the wheel of a pulley. Sheave hole, a channel cut in a mast, yard, rail, or other timber, in which to fix a sheave.
Sheave \Sheave\, v. t. [See Sheaf of straw.] To gather and bind into a sheaf or sheaves; hence, to collect. --Ashmole.
So, I think you can use them interchangeably - but like BigTrees says, some times someone really feels strongly... I had a teacher that say we didn't go to Gym class, or hold it in the Gym - it is called Physical Education, and it is held in the Gymnasium... He kept wanting us to tell him why we were going to Jim's while we were at school, and how we'd have Physical Education in Jim.