Pasture - usually 5-10 acres, can be "fenced & cross fenced"
Field - where they grow crops, not for horses usually
Range - more out west where they have large tracts of land (sq miles) wide open
Run - an attached dirt area behind a barn stall
In & Out - Stall with an attached run
Corrals - small fenced areas for horses, can be for single or multiple horses
Pipe corrals - area for horses that is enclosed with panels made of pipe rather than fenced
Mare Motel - Pipe corrals that have a "roof" over the top of them, usually configured so that at least 12 ft of the corral is covered, aisle is covered and 12 feet of the corral across the aisle is covered. Real handy in climates like AZ & So Cal.
Don't use Paddock or Yard, unless I really do turn them out to mow the grass in my front or back yard. Rarely use pen, unless referring to cattle.