A group is a collection of entities. If you make a bolt, for example, you can group the geometry and place copies of your bolts here and there. However, each group is a separate set of duplicate geometry. A component is exactly like a group except that it is only defined once. Each copy is only a reference to the geometry with enough information to place it and scale it. If you edit a component, all the copies will change as well. This is handy if you want a 12mm bolt and later want it to be a 13mm bolt. If one of your components needs to be different, you can make one of the components into a “unique” version and from then on, it is no longer linked to the previous definition. Its copies will then become a separate set of components. A group can not only contain geometry, but other groups as well (or sub-groups, for that matter). A flywheel might have several groups that make up the separate pieces and then all of them would be grouped to be the flywheel. Also, a group or component can later be “exploded” to remove the outer layer of grouping.
Technically speaking, Sketchup is a surface modeler, but only for planar surfaces. It does not natively support other surfaces such as ruled surfaces, surfaces of revolution, b-surfs, etc. However, each of these surfaces can be approximated by a mesh of planar “facets”. Similarly, SketchUp is not a solids modeler since it has no native primitives such as a sphere, cone, cylinder, etc. However, once again, each of these can be approximated with a mesh of planar facets. If the mesh follows certain rules and encloses a closed volume, then it is considered a “solid” and will treated as such by 3D printing systems.
A line is called an edge in SketchUp. A circle is defined by points, but is technically a series of edges (or segments). An arc with 6 edges will be defined by 7 points. The more points, the smoother the arc, but SketchUp will “smooth” or “soften” them to make them look very smooth when rendered visually (not so much when 3D printing). BTW, under the hood, a circle or arc can be later edited to change the radius or the number of edges … once it has been “exploded” however, it will turn into a series of separate edges and no longer act like a single unit.
A face is a planar surface bounded by a closed loop of edges. When you create a closed loop (like a circle) SketchUp will automatically fill in the planar surface. Due to using a plane as the underlying geometry, most intersections and other 3D manipulation is very fast due to the math involved dealing with direct solutions.