Adaptive Reuse:

Refers to the recycling of an old building for use other than that for which it was constructed. A neutral term, it can involve a sensitive rehab that retains much of the original character (especially on the exterior), or it can involve extensive remodeling.

Preservation:

Is an umbrella term that has meant keeping an existing in its current state by a careful program of maintance and repair.

Reconstruction:

Rarely relevant to homeowners, involves re-creating a historic building that has been damaged or destroyed, by erecting a new structure resembling the old as closely as possible.

Rehabilitation:

Is the most common approach for private houses. It means making a structure sound and usable, bringing it up to modern operating condition while retaining what the feds call "character-defining features. It does not attempt to restore any particular period appearance. Rehabilitation might include new HVAC systems and an updated kitchen, yet retain the stair hall, fireplace, cornices, paneled walls, etc on the interior. The exterior may replace the clapboards with cement board, yet keep the original porches, doors and trim moldings.

Remodeling:

Involves changing the appearance, and usually the style of the structure by removing or covering original details, and substituting new materials and forms.

Renovation:

Is similar to rehabilitation, but assumes the introduction of more new materials or elements to the building. For example, adding not only the cement board, but replacing the original windows with modern windows and storms, insulation, stripping and re-painting.

Restoration:

Is a widely misused term, has a specific meaning in the museum world: the meticulous return of a building to its exact appearance during a chosen period. The National Park Service says the restoration is the "act or process of accurately depicting the form, features, and character of a property as it appeared at a particular period of time by means of the removal from other periods in its history and reconstruction of missing pieces from the restoration period".

Most homeowners need not worry about the restoration process in its purist sense. When the word restoration is used in the context of a private house, it refers to sensitive rehabilitation:
Making the structure sound and usable without extensive reconstruction, but retaining original style and elements.

Interpretive Restoration:

This involves keeping all the original architectural features intact and reconstructing the missing elements as faithfully as the budget allows over the life time of the homeownership.
Interior Decoration, furnishings and exterior paint scheme do not attempt to duplicate what was actually there, but follows your personal taste.  It's more of a do no harm, leave it better than you found it approach.

Remember in the real world, old-house owners use a combination of approaches. Purists sniff that this is what ruins the historical record, but they are not being realistic. Buildings have always been changed for current use. Privately we may restore the exterior elements and landscaping, rehabilitate the 1930's bathroom, renovate the kitchen, and use interpretive restoration for the exterior paint colors.

Post Construction Information:

Operations and maintance manual, construction drawings, measured drawings, field sketches, as-built drawings, and possibly the project files. They include changes in construction different from design drawings. 

Record of Treatment:

New materials and replacement features should be recorded in place with photographs or drawings that clearly show their extent. Physical evidence of the development history of a structure should also be recorded before being removed or covered during the project. Contracts must be clearly written and specific. Any changes clearly marked and included. Pricing documentation. Specifications that were followed, All changes made during a project are graphically documented with cleanly marked drawings and photographs. Video tape including narrative is becoming the new standard to the more progressive field operatives. Customer narrative, maintance updates.

The Purists' View: (not Holly or John's view, just a definition!)

The object of every repair should be the faithful restoration of those features of the original building which yet remain, and their preservation from further injury..And no alteration should be attempted which is not the renewal of some ancient feature which has been lost, or absolutely necessary for rendering the building suitable to the present wants of the building owner; and this should be done in the strict conformity with the character and intention of the building.  

To restore is to revive the original appearance lost by decay, accident, or ill-judged alteration. We must, whether from existing evidences or from supposition, recover the original scheme of the edifice as conceived by the first builder, or as begun by him and developed by his immediate successors; or, on the other hand, must retain the additions and alterations of subsequitions ages, repairing them when needing it. 

Always do less rather than more. When in doubt, seriously consider doing nothing. As Ruskin advises, better to let the building die than live as a fake.