I would say on pictures and writings posted online, the formality becomes less important than in face-to-face conversation. A captions on a picture is a rather private thing, not really addressed to anyone per so, so to be formal in a caption would be too much. On twitter, one would be more formal than in a picture caption, but it depends on who you are. If you are a famous figure with lots of people following you, you would have some formality since you are in a way addressing the public at large. On the other hand, if you mostly have friends following you, you could be just as informal as when you're talking to friends. The formal style is for when you talk to a stranger or address a large group of people like in a lecture or broadcasting. Similar principle applies online as well, but people don't follow it as much when they're online. In fact there seems to be too much bad language and bad manners online unfortunately.