Educational training tends to the vocational or practical and relates to specific useful skills. It forms the core of apprenticeships and provides the backbone of content at technical colleges or polytechnics.
Sporting training appears more mechanistic: planned suites of regimes develop specific skills or muscles with a view to peaking at a particular time. A specialized field of training often used in sports is autogenic training.
Training & Development is the field concerned with workplace learning to improve performance.
In meteorology, training is when a successive series of showers or thunderstorms moves repeatedly over the same area, usually causing some form of flooding, especially flash floods. Often, this happens when a line of rain or storms forms along a stationary front, and moves down the length of the front, while the front is stalled. It is named so because this is similar to the way train cars move down a track in a line, over and over the same point, without the track moving.
In military, training means to drill and keep in shape in case of deployment orders (i.e. the same as exercise, only it's for military units). Also, in an archaic sense, it means to get on trains to transfer from one area of a continent to another (the term was used this way mainly in the American Civil War).