EMSIA = Extended Mobile Suit in Action. Mid-range, good quality toys (ABS?) that's good to play with and to pose. Generally good value for money. Generally in 1/144 scale, and has a fair range. When combined with the basic MSIA line (which it is a bit better), the range is quite exhaustive.
HCM-PRO = High Complete Model PRO. Mid to High range, high quality models (styrene). Completed model almost out of box (minor assembly needed), good for poses but not really for playing with. Somewhat good value for money, but primarily for the looks. Generally in 1/200 (or 1/220, I forgot) scale, and there's a limited variety (but its growing).
In essence, EMSIA = toy, HCM-PRO = model. The differences isn't that clean cut, and the quality is quite close, but that's the key difference.