The .38 Special revolver and the .380 pistols are both often capable of firing the same types of bullets. The rounds for the .38 Special typically have a longer case, which allows them to be loaded into the longer cylinder of the .380 pistol as well as that of the smaller .38 revolver. Though you may imagine that bullets are just bullets, there are several different types of bullets that can be found in the .38 Special caliber.
Standard bullets are the most widely used type of ammunition and consist of a simple homogeneous heavy metal core -- typically lead or a lead alloy -- surrounded by a thin layer of copper. These bullets are usually round-tipped and will flatten slightly when they strike a target, though not as much as a hollow-point bullet might. They are essentially the middle ground between a hollow-point bullet and a jacketed bullet in terms of penetrating and stopping power.
Full Metal Jacket
The full metal jacket rounds are designed to penetrate a target and not expand as they continue forward. They are constructed using the same core as standard rounds but are completely jacketed with an outer layer of metal to prevent them from expanding once they strike something solid or semi-solid. FMJ rounds are typically used against armored targets and usually are illegal for civilian use for this reason.
Hollow-point bullets are designed much like standard bullets, except their tips are hollowed out. These bullets are designed to strike a target and expand outward as soon as they hit, creating large holes in whatever they were aimed at. Hollow-point rounds typically have lower penetrating power, but have far greater stopping power than standard rounds or FMJ rounds because of their expansion. Hollow-point bullets are often recommended as home-defense loads because of their stopping power and lower penetration.
Glaser Safety Rounds
Glaser rounds are somewhat similar to shotgun rounds in construction. Rather than a solid core, the bullet is designed with a number of small pellets encased in a bullet-shaped mold of copper or a similar metal. When fired, the bullet strikes the target and shatters, sending the pellets it was holding into the target. This creates enormous stopping power but very low penetrating power. Glaser safety rounds were designed for use against unarmored targets in urban settings, as the rounds themselves do not typically have enough power to penetrate the walls of a house or apartment and threaten any bystanders outside.