According to Wikipedia:
A classical order is one of the ancient styles of classical architecture, each distinguished by its proportions and characteristic profiles and details, and most readily recognizable by the type of column employed. Three ancient orders of architecture—the Doric, Ionic, and Corinthian—originated in Greece. To these the Romans added the Tuscan, which they made simpler than Doric, and the Composite, which was more ornamental than the Corinthian.
Well said Wikipedia. Classically speaking there is also the order that results from the application of classical elements establishing the interior architecture. The Architecture of the Classical Interior (Classical America Series in Art and Architecture) by Steven W. Semes, is the architectural model for the conception and treatment of classically designed rooms. The addition of columns to interior space definitely contribute to the feel of ‘Classical Order’.
The Doric order originated on the mainland and western Greece. It is the simplest of the orders, characterized by short, faceted, heavy columns with plain, round capitals and no base. With a height that is only four to eight times its diameter, the columns are the most squat of all orders. The shaft of the Doric order is channeled with 20 flutes. The capital consists of a necking which is of a simple form. The echinus is convex and the abacus is square.
The Greek forms of the Doric order come without an individual base. They instead are placed directly on the stylobate. Later forms, however, came with the conventional base consisting of a plinth and a torus. The Roman versions of the Doric order have smaller proportions. As a result they appear lighter than the Greek orders.
The Ionic order came from eastern Greece. It is distinguished by slender, fluted pillars with a large base and two opposed volutes (also called scrolls) in the echinus of the capital. The echinus itself is decorated with an egg-and-dart motif. The Ionic shaft comes with four more flutes than the Doric counterpart (totalling 24). The Ionic base has two convex moldings called tori which are separated by a scotia.
The Ionic order is also marked by an entasis, a curved tapering in the column shaft. A column of the ionic order is nine times its lower diameter. The shaft itself is eight diameters high. The architrave of the entablature commonly consists of three stepped bands (fasciae). The frieze comes without the Doric triglyph and metope. The frieze sometimes comes with a continuous ornament such as carved figures instead.
The Corinthian order is the most ornate of the Greek orders, characterized by a slender fluted column having an ornate capital decorated with two rows of acanthus leaves and four scrolls. It is commonly regarded as the most elegant of the three orders. The shaft of the Corinthian order has 24 flutes. The column is commonly ten diameters high.
Had to include the lovely piece with its corinthian columns.
I feel the Classical Order in all these examples.