get into / get out of

cars, taxis and small boats such as canoes or rowing boats

get on (to) / get off

the tube, trains, busses, planes, larger boats,
bikes, motorbikes, scooters, horses, camels, etc

• I wouldn't get into his car, if I were you. He's a terrible driver.
  
  
• I didn't feel safe in the canoe and wanted to get out as soon as possible.
  
  
• I got off the train when I learnt that it wasn't stopping at Oxford.
  
  
• I had to change at Reading and getting on (to) the right train was a nightmare - there were so many platforms.

Before a preposition or an adverbial particle (like off or up or out), get almost always describes movement of some kind.

Here are some examples of other contexts and meanings where we can use get into, get out of, get on, get on to and get off. But note that movement is implied in all of them:

• I always find it hard to get out of bed in the morning.
  
  
• I didn't want to get into trouble so made sure I completed the project by the weekend.
  
  
• Thanks for the coffee, but I'd better get on. I've got lots to do before lunchtime.
  
  
• We got on very well. We had similar backgrounds and had been to the same school.
  
  
• When we got on to the subject of ambition, I didn't know what to say as I don't have any.
  
  
• They were trespassing. There is no footpath here and I told them to get off my land.