A point is a vertical measurement of type that is .0138”, or approximately 1/72 of an inch. In other words, there are approximately 72 points to the inch.  All type is designated in points (10 point Caslon, 24 point Baskerville, etc.).  Points are always used to specify the size of type.  Typefaces may be set in sizes from four to 144 points, but are generally used in six to 72 points.  Line spacing is also specified in points (two points of leading, etc.).

A pica is a linear measurement of type.  There are 12 points to 1 pica and approximately 6 picas to 1 inch.  The length of a line is specified in picas, as well as depth (height) of a type area.  For example, a given block of copy is to be set 20 picas wide by 36 picas deep (high).  Inches are never used in type measurement.  

An agate line is a measurement used by newspapers to sell advertising space.  There are 14 agate lines to an inch.  An agate line refers to the space occupied by one line of agate type in one column.  The width of the column can vary from paper to paper.  A 60 line ad can take several forms: 60 agate lines in one column, 30 agate lines in 2 columns, etc.