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.