Is that old building historical? Do you belong to a historic society? Well, that depends; if the old building also references a past event, then it might be historical. If that society has been around for a long time, it may be historic. More often than not though, You mean to say "historic building" and "historical society".
Webster's defines the two words as;
a : famous or important in history <historic battlefields>
b : having great and lasting importance <a historic occasion>
c : known or established in the past <historic interest rates>
d : dating from or preserved from a past time or culture <historic buildings> <historic artifacts>
a : of, relating to, or having the character of history <historical data>
b : based on history <historical novels>
c : used in the past and reproduced in historical presentations
The subtle difference in definition is that something Historic is something that dates from the past that had an important impact on history. Historical simply refers to the past.
The Grammarist puts it like this: Buildings, villages, districts, and landmarks deemed historically important are often described as historic because they are historically significant in addition to being of or related to history. Societies dedicated to recognizing and preserving these things are called historical societies because they are concerned with history but not momentous in themselves.
So, an old building (let's say 50 years old or older), is Historic. A society whose mission relates to history, would be called a Historical Society.
But then, what about the term Historic Preservation?
The nuance in usage helps to clarify this apparent contradiction; after all - we are not necessarily referring to important preservation actions that took place in the past, we are referring to programs that deal specifically with historic properties. This is, in fact, why we use Historic and not Historical in the term Historic Preservation - Just think of it as having a silent word like "Environment" or "Places" or "Building" thrown in between Historic and Preservation.
Of course, the current trend in the profession is a move away from the term Historic Preservation altogether and towards the term Heritage Conservation. Not only does this avoid the tricky use of Historic, but it also avoids issues with defining the silent middle word and the word Preservation, which often conjures up images of retirees determinedly trying to "preserve", in all of its historical accuracy (or is that historic accuracy), some great high-style Victorian manse.
Heritage Conservation gets right to the heart of what the field is about: Conservation is to use in a way that does not deplete and Heritage can include the tangible and intangible, the built and the unbuilt, the historic and the modern... Heritage Conservation is the professional field concerned with figuring out how to use, in the most appropriate way, the things we consider important to our shared history.