How can I compare and contrast the behavioral or human relations approach and the classical approach to management?
The classical and behavioral approaches to management (the latter has also been called the "human relations" approach and the "neoclassical" approach; these are all basically the same thing, though some people consider the "human relations" form to be an older version whereas "behavioral" is the modern method) are similar in many ways. Both are intended to optimize productivity of workers, and hence profitability of companies. They both assume a hierarchy of managers over workers in which managers tell workers what they should do, and of course they both assume the context of a capitalist economy where companies own capital, hire workers, and make profits. (It's important to remember that neither of those things are actually a given; worker-owned co-ops are quite common in many places, and for most of history most of the world has not been capitalist.)
But the classical approach is extremely hierarchical; that is essentially its defining feature. The whole structure is based around ensuring discipline and an orderly chain of command. You have clearly defined objectives, quotas to meet, and rewards and punishments tied directly to whether or not you fulfill those objectives. By design, managers are not supposed to be friendly with their workers, as this is "unprofessional" and could undermine discipline. Rules must be followed exactly, and if they aren't, the punishment must be swift and severe. The place you'll see the classical approach used the most nowadays is actually the military---though even they are starting to figure out its shortcomings.
The behavioral approach relaxes the hierarchy a little bit, without eliminating it entirely. Based on empirical research showing that happy and motivated workers perform better (managers aren't doing this out of the goodness of their hearts, for the most part; they expect higher profits to result), the behavioral approach involves providing workers with a pleasant, friendly environment and much heavier focus on teamwork and cooperation rather than cooperation and individual rewards.
The behavioral approach also encourages feedback from workers to managers about what is working and what isn't, making the system more flexible to change and better at improving itself when things go wrong. Whereas a classical manager would punish criticism as insubordination, a behavioral manager would try to understand the criticism, and either implement the proposed changes or at least do something to address the problems that the workers noticed.
Classical management also involves a lot more direct monetary incentives (e.g. a commission on sales or a bonus for exceeding quota), whereas behavioral management emphasizes non-monetary incentives (e.g. "Employee of the Month" and praise for a job well done). These tend to be cheaper for the company and can be just as motivating for workers, though it's legitimate to ask whether it is fair to workers for managers to reap all the monetary gains while workers just get a pat on the back.