The following terms have been widely used to characterized the phases of quantum matter or the gauge theory:

i. **Long/short range order, **

ii. **long/short range interactions, **

iii. **long-short range entanglement**

How are they different from each other?

Can one give examples for certain phases of matter that has **long/short range order, long/short range interactions, long-short range entanglement** for each choices of long/short? There are totally $2^3=8$ possible characterizations in terms of these terms.