First, they're all polearms (AKA hafted weapons, staff weapons). Some writers will use "polearm" to mean "hafted weapon other than spear/pike", but properly speaking, they're all polearms.
It's difficult to precisely define a spear, since there are spears with unedged conical points, single-edged heads, double-edged heads of various forms, and multi-pointed heads. Spears vary in length from a few feet through to 18 feet even for spears that aren't called pikes. Some spears have heads capable of cutting, so not all are purely thrusting weapons. If it is a hafted weapon with a simple thrusting head, it's a spear, but there are other spears that aren't so easily described.
A pike is simply a long two-handed infantry spear, often 15-25 feet long. However, it can refer to weapons as short as about 10' (but these are also sometimes called "half-pikes", so "pike" in this case is a shortened form of "half-pike"), such as, e.g., naval boarding pikes (really anti-boarding pikes).
"Lance" is often (but not exclusively) used to distinguish cavalry spears from infantry spears and pikes.
Waldman (2005) defines a halberd as:
a cut and thrust combination staff weapon, consisting at first of an elongated axe-like blade, early forms of which are sometimes described as knifelike, from which a vertical spike of varying shape and length arises.
although some late halberds don't have elongated axe-blades, and this definition would also include pollaxes (since it says nothing about back spikes or hammer faces).
A glaive has a long cutting head. Sometimes the tip of the cutting edge is an acute thrusting point in line with the haft, and sometimes the curvature of the blade means that thrusting end of the blade presents and edge rather than a point. (What is the difference between a single-edged spear and a glaive? The glaive has a long cutting blade, and a single-edged spear has a (usually short) thrusting blade that might be no more useful for cutting than a typical double-edged spearhead.) A key difference between halberd and glaive is that the halberd has a separate thrusting spike, and that on a glaive (if it has a pointy tip) is simply the end of the cutting edge. But there are early halberds with blades of a similar form, with the thrusting point being the end of the main cutting edge; these are classified as halberds because the head is attached to the haft by two eyes rather than the single socket of a glaive, as noted by Waldman:
The glaive is a large cutting and thrusting weapon whose shaft can be up to 2 meters (6’ 6”) in length. The blade edge is convex, the back is usually straight, but may be slightly concave. The shaft socket is central (unlike the similar appearing vouge) and basal lugs may be present. [...] The name glaive, however, has been the source of confusion for a long time.
To these definitions, we can add the bill, with a concave cutting edge (straight bottom section with a curved forward top edge). Some halberds have concave cutting edges too, and can be distinguished from bills by their more axe-like appearance.
It's possible to find difficult-to-classify polearms that some would call spear and others pike, some would call halberd and others glaive, halberd and bill. If we add in partisans, vouges, bardiches, axes, etc., it gets worse. For example, is the weapon on the left here:
an axe or a halberd, and the one on the right a halberd, a glaive, or what? (Snook says "halberd" to both.)
When it comes to English names for non-European polearms, there are inconsistencies. For example, the naginata and guandao are often called "halberds" when "glaive" would fit the classification scheme for European polearms.
Accept the classification of polearms as imprecise, with ambiguous and intermediate examples of weapons to be found. In most cases, the classification is reasonably clear, but there are many exceptions. Different writers will use different names for the same weapons, and use the same names with different meanings. In the case of extreme ambiguity, there is always the generic term "polearm"!
References:
Snook, George A., The halberd and other European polearms, 1300-1650, Museum Restoration Service, Alexandria Bay, N.Y., 1998.
Waldman, John, Hafted Weapons in Medieval and Renaissance Europe: The Evolution of European Staff Weapons between 1200 and 1650, Brill, 2005.
