In a bell and spigot joint one end of the pipe stick is flared, termed the bell or socket, to enable the opposite end of the next stick, the spigot end, to be inserted to create a joint. The gaps in these joints were stuffed with oakum or yarn to retain molten-lead, which solidified into a waterproof joint.  This was a labor-intensive operation, and the quality of the seal was dependent on the skill of the laborer.
Mechanical joints were made by bolting a movable follower ring on the spigot close to the corresponding bell, which compressed a gasket in between.  Many water pipes today use mechanical joints, since they are easily made and do not require special skills to install.  This type of joint also allows some deflection to occur without sacrificing joint integrity, so that minor alignment adjustments can be made during installation, and the joints retain their integrity when subjected to limited subsidence.  Typical joint deflections at mechanical joints today range anywhere from 3 to 5 degrees.
Ball-and-socket joints introduced more "rounded" sockets, allowing a relatively large amount of deflection at each joint.  This type of joint, still in use today, was considered a special-purpose joint, and has been used primarily in both submerged and mountainous terrain.  This type of joint can typically allow around 15 degrees of deflection at each joint, making snaking of the pipe possible.  The advantage of this joint type was that it was quicker than bell and spigot joints, and did not require special skills or tools to install.
Push-on joints, developed in the mid 1950s, allowed a quicker and relatively non-skilled method of jointing pipe.  This joint consisted of a bell with a recessed groove which held a rubberized gasket.  A lubricated beveled spigot section can be pushed into this joint with care, as not to roll the rubberized gasket, and once installed became watertight.  This type of jointing system is popular today with ductile iron and polyvinyl chloride (PVC) pipes.