Scimitars (pronounced "sim-i-tar") are a type of slash weapon that can also be used as a stab weapon, although less effectively. They can deal slightly higher hits than swords, but less than longswords.
Scimitars have exactly the same attack speed as daggers and claws, but provide a higher attack bonus than daggers and yield lower defence bonuses than claws. The combination of high attack and swing speed give the scimitar its large popularity in melee training.
Most types of scimitars are made with the Smithing skill, purchased at a scimitar shop identified with the scimitar icon on the map, or traded through other players.
In short, scimitars have better DPS against most monsters than longswords and are better suited for PvM and training melee stats. Longswords have slightly higher strength bonuses which gives them higher possible maximum hits. Overall, it is recommended to get a scimitar over a longsword whenever possible.
The scimitar and longsword are very similar weapons as they are both slash weapons and have nearly the same attack bonus for slash. However, scimitars have an attack speed of 4 while longswords have an attack speed of 5. This lets scimitars attack 1 tick (about 0.6 seconds) faster. Longswords have slightly higher strength bonuses than their scimitar counterpart, which gives them an additional +1 to the maximum hit.
Comparing the two weapons, the scimitar will hit 25% faster in exchange for 1 damage to the max hit. This makes them better to use than the longsword in most situations.
It gets more complicated as other factors come into play, such as enemy's defence bonuses, the player's Attack and Strength levels, and the player's attack bonuses from other gear. As a simple example, dragons are relatively weak to stab. Longswords have a much higher attack bonus for stab than scimitar and will do more DPS, assuming the player is using the stab attack style on the scimitar. Scimitars will still do more DPS to dragons than longswords if the slash style is used for the scimitar, even if the longsword is used on stab.