Carrying capacity is the amount of life (i.e, population) a specific area can reasonably sustain over a long period of time. Limiting factors are those factors that affect whether or not a population grows or decline. A population can temporarily exceed the carrying capacity, but there will be negative effects iF the population is not reduced.
For example, think of an elevator. The carrying capacity of a particular elevator might be 10 people. The carrying capacity is limited in this instance by lack of available space; and also probably weight limit. You may be able to squeeze more than 10 people into an elevator for a brief amount of time, but the result will be overcrowding, feelings of grouchiness, and possibly too much strain on the mechanisms that keep the elevator from falling.
