Preemie (Premie):

In humans, preterm birth refers to the birth of a baby of less than 37 weeks gestational age. The cause for preterm birth is in many situations elusive and unknown; many factors appear to be associated with the development of preterm birth, making the reduction of preterm birth a challenging proposition.

Premature birth, commonly used as a synonym for preterm birth, refers to the birth of a baby before its organs mature enough to allow normal postnatal survival, and growth and development as a child. Premature infants are at greater risk for short and long term complications, including disabilities and impediments in growth and mental development. Significant progress has been made in the care of premature infants, but not in reducing the prevalence of preterm birth.^[1] Preterm birth is by far the most common cause of prematurity, and is the major cause of neonatal mortality in developed countries. Premature children may commonly be referred to throughout their life as being born a "preemie" or "preemie baby".

Source: Wikipedia

Micro-Preemie:

A baby that is under 1 ¾ pounds (between 700-800 grams) and is generally born before 26 weeks gestation, some sources will broaden that range to include all babies up to 3 pounds.