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:
There is a feature that some people think distinguishes the two Redeyes but it does not: the presence or absence of a separate black dot forward of the spur on the side of the thorax, present in the Small Redeye but absent in the Large Redeye. Here, on a “Myth Buster”, are counter-examples of both.
My comparison [above] 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.