In Europe there are three Erythromma species, the so-called Brighteyes. Two of these have red eyes and occur in the UK. The third, bucking the family trend, actually has blue eyes and hence is called the the Blue-eye (Erythromma lindenii). The British vernacular name for the Blue is the rather ungainly [personal opinion] Goblet-marked Damselfly.

The Blue-eye does not occur in the UK. Thus, in the UK we are left with the two red eyed species which are readily confused, the Large Redeye/Red-eyed Damselfly (Erythromma najas) and Small Redeye/Small Red-eyed Damselfly (E. viridulum). Hopefully this will clarify the distinguishing features:

Comparison: Redeyes

That comparison is based on mature colouration. Someone asked about the colour variations from immaturity through to maturity so here are maturity variations of both male and female Large Redeyes:

Large Redeye Maturity Variations

In continental Europe, the Blue-eye (E. lindenii) is more readily confused with the Common Blue Damselfly/Common Bluet (Enallagma cyathigerum), in my experience.