Keywords, for clarity.
Up front, the issue is simple: There need to be separate terms for Movement Slows and Attack Speed Slows. Right now, they are both called "slow."
Just for the sake of comparison and to solidify the concept I am talking about, let's use Magic: The Gathering as an example. Way back in the earlier stages of the game's life, a card would tell you its special effects in the text box under the artwork. There was a standardized "phrasing" for certain things. Later on, these effects were simplified into "keywords." A few examples:
First Strike Creatures with first strike deal damage before other creatures in combat.
Haste Creatures with the haste ability are able to attack and use abilities... on the turn a player gains control of them. (They don't suffer from "summoning sickness.)
Flash Artifacts, creatures or enchantments with flash may be played any time their controller could play an instant.
Trample Creatures with trample may deal "excess" damage to the defending player if they are blocked.
As you can see, this is important for two main reasons:
- Clarity (Don't have to explain all the effects of a card like Akroma when keywords do that in a small space)
- Quickly reading and understanding a card "at a glance."
So how does this translate to League? League already has a set of keywords people are familiar with... AD, AS, LS, Crit %, Crit Mult., ArPen, etc (just to name a few). However, there are two kinds of slows that are both named... slow.
Starting with an example of something that does both, 
W (Wither): Nasus ages the target enemy champion, slowing their movement speed by 35%, increasing over 5 seconds, and their attack speed by half the amount for the duration.
What about 
? Does both, right? These examples are as old as the game itself, so it's easy to see why these types of slows may have been lumped together, but we also have effects that only do one or the other.
E (Lucent Singularity): _ Lux sends an anomaly of twisted light to the target area, slowing nearby enemies and granting sight of the area around it for up to 5 seconds._ Only movement speed is slowed.
: Reduces the attack speed of nearby enemies by 15%. Only attack speed is slowed.
My suggestion for the keyword itself is from my first example: Wither. Something like Exhaust would read as "Slows and Withers the target 35%, blah, blah, blah..." Obviously, it can be any word which clearly and quickly explains its meaning, but this is just to start the discussion.
As a bonus, can you guys think of other effects which should/could have a keyword to clarify and simplify the text on items and abilities?
