Since most handguns are intended for short ranges (less than 50 yards) and are fired at relatively low velocities, the bullets do not have to be held to the same standards as rifle bullets. A pistol bullet is held to far different accuracy standards than a rifle bullet. A rifle bullet should be capable of shooting 3 shot groups less than 1 ½ at 100 yards to be considered accurate. A pistol bullet that produces 3 shot groups of 1 1/2 at 25 yards is considered to be outstandingly accurate.
Pistol bullet construction is generally Full Metal Jacket (FMJ), Jacketed Soft Point (JSP), Jacketed Hollow Point (JHP) or unjacketed lead.
FMJ bullets for handguns are usually either round nose or flat nose. The quintessential FMJ round nose is the .45 ACP ball load. The 230 gr. bullet is designed to give reliable feeding and relies on mass to damage the target. FMJs generally started life as military loadings to comply with international laws of warfare but were (and still are) relatively easy to make. FMJs continue to see much use in the civilian world as inexpensive practice ammo.
JSP bullets came into favor when civilian and LE shooters saw that FMJ ammo was less than ideal for stopping an attacker. JSP bullets are more likely to expand in the target and transfer energy rather than pass through the target. Most JSP ammo today is used for hunting where deep penetration is still needed but some degree of expansion is still desired. Few people still use JSP for self defense as the JHP bullets dominate that niche. JSP bullets, while better for defense, still are very lacking in performance on thin skinned targets.
JHP bullets can be either fully, partially or half jacketed. Full jacketed hollow points are generally used in self loading pistols. They attempt to combine the feeding characteristics of an FMJ with expansion superior to the JSP. Partial jacketed HPs are frequently used in revolvers where feeding is less of an issue than it is in the self loaders. Revolvers are much more forgiving of blunt noses with exposed lead at the tip. All sorts of special features are designed into JHP bullets like star shaped cavities, central posts, brass jackets with folded petals, bonded cores, aluminum jackets, reverse tapered jackets and huge gaping hollow points like the Speer flying ashtray.
The intent is to allow the bullet to expand in a controlled, predictable way so it leaves the largest, most incapacitating wound possible while still penetrating deeply enough to reach vital organs. A noteworthy alternative to traditional JHP bullets is the Speer Gold Dot. This does not use a jacket with a core inserted into it. It uses a lead core with the jacket electroplated to it. The hollow point is then formed in what ever configuration desired. The jacket is literally a part of the core at the molecular level. The Gold Dot can withstand tremendous forces with out breaking up. This allows the weight to remain constant for deep penetration while the hollow point size and configuration allow reliable consistent expansion.
Unjacketed bullets are generally either cast or swaged. Cast bullets are generally harder but it depends on the specific alloy used. Cast bullets can be in any number of point configurations such as round nose, wadcutter, semi-wadcutter, flat point, rounded flat point, and truncated cone. Each has a specific purpose. Many are available with gas-checks. A copper cup crimped to the base of the bullet to prevent the hot gasses generated by the burning gun powder from melting the base of the bullet. Hardness can span the range from fairly soft to extremely hard (linotype) depending on the intended use.
Swaged bullets are normally soft pure lead as this metal is easy to work with. They are made from lead wire cut and pressed into a specific shape. Some hard swaged bullets have become available recently that combine the ease of manufacture of the swaged bullet and the more desirable hardness of a cast bullet.
As mentioned earlier exposed lead at the base of the bullet can allow hot gasses to melt and vaporize some of the lead allowing it to stick to the barrel causing leading. The harder the lead alloy, the more resistant this phenomenon the bullet will be. A gas check at the base will prevent most of this problem.
There are many specialty bullets that are not available to the reloader so I will not attempt to cover them here.