The content of a vector mask (or a shape layer) is called a Shape. The Shape consists of several Paths. A Path consists of multiple Knots. Each knot consists of three points: the anchor and two handles.
Here we see a shape consisting of four paths. The path on the right consists of five knots. The knot consists of an anchor (in the middle) and two handles.
There can be several paths within a shape. Paths have a fixed order (the first, the second, the third ...). Each path has some boolean operation, which defines, how the path (e.g. the fourth path) is combined with the content under it (i.e. paths 1, 2 and 3). Boolean operations are Union, Subtract, Intersect and Exclude.
Here we see four shapes with two paths in each shape. The second path (the ellipse) has different boolean operations.
When all paths have the Union operation, their order is not important. But e.g. when some path has a Subtract operation, reordering paths may produce a different result.
Paths can be open or closed. Open path means, that the first and the last knot are connected with a straight line (ignoring the adjacent handles).
A path consists of a sequence of knots. Each two consecutive knots are connected with a curve segment, that is shaped by adjacent handles. A knot can be linked / smooth (both handles are located in a line with the anchor) or unlinked / corner (handles have arbitrary locations). A linked knot guarantees the smooth curve, while an unlinked knot usually creates a corner.
A linked knot is visualised with a circle anchor, while an unlinked one has a square anchor.
The handle of the knot is collapsed, when it is located at the location of the anchor point. When all knots in a path have collapsed handles, then the path consists only of straight line segments (i.e. it is a polygon).
While vector masks simply hide the portion of a layer, Shape Layers have more interesting properties. Each Shape Layer has a Fill and a Stroke value. Fill and Stroke can have one of four values: None, Color, Gradient and Pattern. Combine different values of Fill and Stroke to create various styles. Have a look at possible combinations.
Stroke can have many parameters: Line thickness, position: Inside, Center, Outside, corner shape, gaps (dashed line) etc. When your shape contains just a single open path, the first and the last knot will not be connected inside a stroke.
Change the look
When any vector tool is enabled (e.g. a Pen tool or a Rectangle tool), the top menu shows the Fill and the Stroke parameters of a current shape layer. You can change these parameters there.