This page has a whole lecture about these two monstrosities (accessed 05/14/2015).
Gosh, what is cytoplasm now? Hah! It's like a liquid container of the other cell constituents made of 80% water. Although, we must know that the nucleus itself is a whole world on its own. The watery mix in the cytoplasm is called Cytosol that contains stuff like Glucose, Salts, Enzymes, CO2, and Oxygen, (plus organlles in eukaryotic cells).
Eukaryotes (bottom picture, an animal cell) on the other hand, are organisms with one or more cells with distinct nuclei and some other special units called Organelles. This type of cells can be found in fungi, plants, and animals (us too). So basically, these eukaryotes have an Outer Membrane, an Inner Nucleus, a mass of Cytoplasm, and the special force organelles!
Just like in chemistry that we deal with fundamental units like atoms and molecules, here we have cells. Cells are the fundamental units of living organisms. This word is so versatile we see it everywhere: solar cells, spreadsheets like MS Excel, and even in prisons! Well we are made of those little units. Again, similar to the atoms, cells have nucleus, in which the core essence of the cell exists; I mean the DNA, the genetic signature of every living creature!
Generally, organisms are either Prokaryotes or Eukaryotes. These fancy-looking words are to categorize cell types. Prokaryotes (top photo, a bacterium cell) are those who do not have a distinct cell nucleus (I presume they don't have one!), such as bacteria or blue-green algae.
The Membrane of the cell is double-layered with Phospholipids, which is a type of lipids (fat, wax, and similar material) that contain phosphorus obviously! Other stuff in the membrane include Proteins, Cholestrol, and Glycoproteins. Plant cells also have another cell protection named Cell Wall which is around the membrane! Many single-celled creatures have something like an extended tail called Flagella they sue to move around. Funny its name is like the red flag truck drivers tie on to their long extended load on their dump sections!
So how big is this cell we are talking about? Definitely way larger than atoms as whatever we talk about is probably made of millions of atoms themselves! They are less than 20 micro millimeters! Wow too tiny I guess! So what determines the size of a cell? Obviously it works like a bus terminal for transporting nutrients and other material through the membrane. The more need for transport creates a bigger sized cell. And since a cell is actually a 3D terminal we are dealing with its surface area which lets the nutrient transporters (whatever they are!) in and out. A larger surface area results in a larger cell volume as well and consequently more of the material that composes the cell itself.