Well I have never heard of these terms used in every day conversation and I am a "vertically challenged person" -- I suggest you get a new research of russian linguist.
Things that would be used for short people to be politically correct would be petite. Lttle person would be used with those with dwarfism.
For fat person - overweight, heavy --
The ones you mention may be used -- but it is typically when making a joke or trying to be funny about being overly sensitive or overly politically correct.