Q:

Why is actual SOC of a battery actually higher than what is displayed

So I read a document today which said that a higher SOC level (around 20%) is displayed as 0% to the user in vehicles, thus reducing the total capacity of the battery.
My question is that why is that done? Why do we limit the depth of discharge? I know for some batteries like NiMH there are memory effects, but why do we do it for other batteries like Li-ion?

A:

The further we discharge lithium batteries, the more damaged they get (a deeper discharge is equivalent to a higher cycling count). This is particularly true for a very deep discharge, where battery voltage decreases rapidly:

Image source: batteryuniversity.com
Keeping the user from discharging the battery to this extend increases battery life time significantly, while not shorting the runtime of one battery charge too much. 
I can't say if in practise it is really as much as 20% of capacity left (this seems like quite a high value), but a certain "safe guard" will keep the battery from going into deep discharge, from which it might not even be able to discover (imagine a user completly discharging the battery and then leaving the device off for several days without recharging. This would surely damage the battery. Shutting down the device at a few percent capacity left will reduce this risk a lot).

The same is true for the upper end of the charging process: If a lithium ion battery is charged to more than 80% the wear of the battery increases. Limiting the charging process to 80% can increase the life time significantly, because the damage done to the single cells when charged to more than 4 V increases as well.
Regarding your comment to memory effect at NiMH:
This effect is quite opposite: You want to discharge these batteries as far as possible, otherwise you will reduce their capacity.

