There are typically three types of possible targets for Spells and Abilities. They can either hit only their target (Single Target), everyone within a certain radius (Area of Effect) of the ability's target, or a set of targets within a certain arc in front of the player/monster (Conal).
The vast majority of job abilities are single-target, as are many monster TP moves. Berserk, Sigh, Protect V, etc. are all single target. They just affect the target of the spell, and that's it. One interesting quasi-exception is Haste Samba, which is a single target ability but indirectly functions as a buff for the entire party.
Area of Effect
Area of Effect abilities always hit players within a certain range of the target, though that range can vary based on that which ability is used and a variety of other factors. For instance, Glavoid's Gorge TP move affects players within about a 13 yalm radius of the monster, while Chloris' Fatal Scream affects all players within a 20 yalm radius of the monster. Monster spells, and some TP moves, are centered on the player target instead of the monster itself. Controlling all of these factors is very important for positioning in some fights.
For players, Area of Effect abilities include spells from Stoneja to Protectra, and the ever-popular Circle abilities. Though many Abilities and spells have constant radius, some can change. For example, String Skill can affect the radius of Songs, and Luzaf's Ring can affect the radius of Phantom Rolls and Double-Ups.
Conal Attacks are generally limited to "Breath" type moves, both from players and monsters. Typically these are either status effects (like Filamented Hold) or damage (like Heat Breath). If they are damage, the damage is often proportional to how "centrally" the monster or player target is relative to the direction the monster is facing. So if you stand in front of a Wyrm when it uses a Breath move instead of on the feet, you're liable to take over 2000 damage instead of ~200.
Wyrms are actually an interesting exception, as their breath moves represent a type of abilities that are both conal and single target, due to their movement restrictions. Wyrm Breaths will always hit the target, even if he is outside of the cone on the Wyrm's feet, but will not hit others nearby that are also outside the cone. However, it will certainly hit other players that are unfortunate enough to stand in front of the Wyrm.
Sort of a sub-type of Conal Attacks are Gaze based attacks. Gaze attacks are generally conal, but also require that the target be facing the monster. Things like Ahriman Hypnosis or Dragon Petro Eyes fall into this category.