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."