I can’t say for abilities but for basic attacks speed is one of the factors used to balance DPS.
So within a given tier you get like
Slow + High Damage
Avg + Avg Damage
Fast + Low Damage(RS 2007 Gold)
The damage rating (dictating what it can do per hit) is balanced against the speed (how often it hits) so that the DPS is equal.
Using unrealistic examples for simplicity sake:
A rapier might do 100 damage and have a 1 second attack speed – Therefore 100 DPS
A sword of the same tier might then have 200 damage and a 2 second attack speed – So once more 100 DPS
A mace would then have 400 damage and a 4 second attack speed – So once again 100 DPS.
Accuracy does come in too to make a three way equation, but it follows the same essence where speed, damage and accuracy are all related to each other to keep the DPS equal across the tier. Eg going back to the above loose simplified examples:
Rapier – 155 Damage, 1 second attack, 65% accuracy – 155 in 1 second gives 155, but accuracy means you do 155*0.65 for 100 DPS
Sword – 200 damage, 2 second, 100% accuracy – equates to 100 DPS. (Runescape 2007 Gold)
Mace – 800 damage, 4 seconds 50% accuracy – 800 in 4 would be 200 in 1, but 200*0.5 for accuracy gives 100 DPS again.
I admit I got no idea how the accuracy numbers in-game translate too actually accuracy % exactly, but this is the principle behind them.