The traditional term "Earth science" signals a focus on geology. The term has been used in other ways also; but Earth system science is focused on the interactions and feedbacks between the atmosphere, hydrosphere, geosphere, and biosphere.
The population of the world is now large enough that humans can have an effect on the Earth system. Extensive deforestation removes a natural sink for atmospheric carbon dioxide, a principal greenhouse gas. Building cities involves sewers and drainage systems that manage water differently than Nature does; involves roads and parking lots that handle solar radiation differently than Nature does. Burning fossil fuels in factories, homes, and vehicles also adds greenhouse gases to the natural atmosphere.
Laboratory science courses are important for learning scientific influences by controlling all other influences except the one under study. But the Earth does not fit into a laboratory, and its multiple influences and effects cannot be controlled. Examining the systemic interactions between the components of the Earth system opens doors that remain closed in the laboratory.
Many complicated mechanics problems discussed in college courses have the default property that nothing happens if no cause is exerted. A billiard ball and cue stick lying still on the lab table provides such a "null" solution. There is never a moment when the atmospheric wind is stationary everywhere. Solar radiation strikes the Earth at systematically different angles: high angles in the tropics; low angles near the poles. This differential heating of the Earth establishes systematic temperature and pressure gradients, such that the atmosphere is constantly in a state of moving toward thermal equilibrium. Whereas this dynamic behavior often appears random to the untrained observer, atmospheric winds blow in a very systematic way based on differences in fluid dynamical forces from one region to another.
While scientists have learned a lot about the fundamental, internal workings of each of the Earth system "spheres", interactions between those once separate disciplines is very challenging. Using the laws of physics to understand why the winds blow is not, by itself, sufficient to understand how birds fly, how rocks weather, how tidal waves come about, nor how humans set priorities.
Ninety percent of getting the right answer is in asking the right question. This is not always easy. In considering the unique presence of water on planet Earth, we marvel at its comfortable presence in solid, liquid and vapor states. To understand the origin of the massive ice caps at the poles, or the systematic rainfall in monsoonal climates, or the global scale movement of water around the planet, we begin with the science of condensation of water vapor into droplets a few millionths of a meter in diameter! If we don't understand how that happens, then we don't really understand water on planet Earth. Earth system science never sets a limit on questioning.