You are more or less correct. "Load" and "pressure" are just a bit different. "Load" suggests something steady that doesn't go away, like the weight on the back of an overworked mule. "Pressure" suggests something very forceful that only lasts for a short time. A student who signs up for six university courses is taking "a heavy course load." A student who gets frantic and upset in the week before the final exam is "suffering from the pressure of final exams."

It's not necessarily under pressure but rather the amount of work they have. A load is something being carried and so it's the quantity of work they are figuratively 'carrying'. Hope that helps. Andrew