Definitions

Overhaul
An engine overhaul means putting the engine back to factory specifications. This generally involves new piston rings, bearings and gaskets. When done by a competent engine builder the engine will perform as new.
A top overhaul only covers the replacement of components inside the cylinder head without removing the engine from the vehicle, such as valve and rocker arm replacement. A full overhaul however covers the whole engine component replacement which requires the engine to be removed from the vehicle, such as replacing the connecting rods and crankshaft bearings. By comparison, a full overhaul service costs more than a top overhaul service.

[edit] Rebuild
Rebuild is a marketing term with no fixed definition. It is often taken to mean a professional overhaul with certain parts replaced with new units whether needed or not. For example some rebuilders will always replace the pistons (which often are not replaced during an overhaul unless damaged).

[edit] Re-manufacture
Re-manufactured is a marketing term to mean an engine put together to match factory specifications e.g. "as new". Although often a buyer may take this to mean all-new parts are used, this is never the case. At the very least, the cylinder block will be used, as may most other parts. High-quality rebuilds will often include new pistons and line-boring of the crankshaft and camshaft bores.

[edit] Blueprinting
In engine blueprinting, all the specifications are double-checked. Usually this indicates closer-than-factory tolerances, with custom specifications appropriate for a street car or a race car. The goals usually are to:
Ensure the engine puts out the rated power (because not all mass-production engines put out the rated power) for its manufacturer's design
or
Make more power out of a given engine design, by extra careful measurement and assembly
balancing of reciprocating parts and rotating assemblies, to reduce engine vibrations thus achieving more power due to recover of power "lost" to vibrations
Ideally, blueprinting is performed on components removed from the production line before normal balancing and finishing. If finished components are blueprinted, there is the risk that the further removal of material will weaken the component. However, lightening components is generally an advantage in itself provided balance and adequate strength are both maintained, and more precise machining will in general strengthen a part by removing stress points, so in many cases performance tuners are able to work with finished components.
For example, an engine manufacturer may list a piston ring end-gap specification of 0.003 to 0.005 inches for general use in a consumer automobile application. For an endurance racing engine which runs hot, a "blueprinted" specification of 0.00045 to 0.00050 may be desired. For a drag-racing engine which runs only in short bursts, a tighter 0.00035 to .00040 inch tolerance may be used instead. Thus "Blueprint" can mean tighter or looser clearances, depending on the goal.