Dragonflies and Damselflies are a fascinating and highly addictive form of wildlife to study, I should know, its all I have done between late April & early November for the last 15 years!!
Demoiselles are our largest and most attractive Damselfly, we have two species in the UK, the Banded Demoiselle and the Beautiful Demoiselle, the Banded is the more common of the two.
In its most basic form the main difference between Damselfly & Dragonfly is the shape of the wings (as explianed above) and the way in which the insect holds them when at rest, Damsels will fold their wings down their abdomen whilst a Dragonfly holds its wings at 90 degrees to its abdomen, this is easily seen in the images below.
Damselfly - Banded Demoiselle
Dragonfly - Four-spotted Chaser
There are lots of other differences between the two, Eye shape/configuration, body shape, etc.... but the wing angle at rest is the quickest way of separating the two, with the one exception of the Emerald Damselflies which tend to hold their wings at about 35 degrees.
I highly recommend you have a good look through our own Dragonfly & Damselfly Gallery
here on WAB, its an excellent rescource for anyone who wants to learn more about these fantastic insects.