FMJ is "Full Metal Jacket" and is used to describe rounds that are entirely encased (except for the bullet base, typically) in a metal jacket, usually copper alloy called gilding metal. FMJ rounds are also sometimes referred to as "ball" (meaning "standard") ammunition by the military. Generally these rounds are designed with little to no expansion in mind. They are comparatively inexpensive to produce, feed well, give good penetration in most materials. The jacketed nose prevents bullet expansion and typically leaves the bullet intact after striking flesh (the 5.56 round is a notable exception).
JSP is "Jacketed Soft Point" and is used to describe rounds that are encased in a metal jacket, again, usually gilding metal, but leave the soft lead core exposed at the tip of the bullet. The soft nose deforms upon striking dense mediums, and these rounds are generally designed to expand rapidly at the nose and mushroom, ensuring that the center of gravity stays in front, and causing the bullet to continue traveling forward through the target. The larger frontal surface area causes more tissue disruption compared to most non-expanding bullets.
JHP is "Jacketed Hollow Point" and is used to describe rounds that are encased in a metal jacket, gilding metal again, but have a small cavity in the nose along with a round opening in the jacket in the nose. JHP rounds are also designed for expansion but tend to have faster "mushrooming" effects because the hollow point is filled with high-pressure material when the bullet impacts, often peeling back the jacket and making a "mushroom" shaped projectile.
BT stands for "Boat Tail" and refers to the base of the bullet. A "Boat Tail" is a sloping end which narrows gently at the base of the bullet, so that the cross-section resembles the shape of a boat's hull. The boat tail shape reduces drag on a bullet, helping it to retain velocity and resist deflection from crosswinds, but causes the bullet to take longer to "settle" after leaving the barrel compared to a standard "flat-base" bullet. Boat tail bullets are usually selected for long-range shooting, while the flat-base bullet shape tends to be more accurate at short ranges. A "HPBT" bullet is a "Hollow Point Boat Tail" bullet.