It's more of a shortening of terms. Its full name / phrase should be "Television Mini-Series' (or 'Miniseries', if you're American like that). We simply say 'mini-series' in the same way that we simply say 'series' instead of 'TV series'.
According to Wikipedia, "a mini-series is a television program that tells a story in a predetermined, limited number of episodes." To elaborate: a miniseries is distinguished from an ongoing television series: the latter do not usually have a predetermined number of episodes and may continue for several years.
Usually, an easy way to determine whether it is a series or mini-series is whether it advertises 'Seasons' of itself. If it intends / has seasons, it is a series. Without it, it's a miniseries.
In terms of whether there are theatrical miniseries as well, I'd say no. Movies are usually standalone features, and even when there is a direct following movie it is referred to as a sequel rather than part of a miniseries.
Some examples of each include: