Paul, both are used. There is no functional difference I'm aware of:) I use both... rather even by mood than by taste. The second one is actually similar to lover-case Greek delta (see delta in Wikipedia). In modern schools kids are only taught 'g' version. By upper grades they adopt individual hands. Some shapes they adopt result from simple convenience. They invent others based on esthetic consideration, and they 'borrow' some that they have spotted someone using. There are shapes that are in use since at least 19th century, even though you won't meet them in "прописи". But check here, page 3, lines 3-4. http://calligraphy-expo.com/aboutcalligraphy/manuscripts_rgb/samouchitel-rukovodstvo-k-samoobucheniyu-pismu-angliyskomu-krasivomu-tetrad-7 Seems like in 1902 'delta' shape was taught alongside with g-like. I'm curious myself, if there were any considerations as to when to use which... E.g. соседка ('g-like') and подруга(delta-like).

In typing, the italic version of the lowercase д usually looks like the lowercase English d. As for handwriting, it's a matter of personal style. Writing lowercase д like English g is considered a standard and that's how it's taught in schools.