Actually no, binding is preventing or forcing a physical or spiritual being to do thing against their will at your will. Most frequently used against harming you or anyone else. But it is also used to create ties that allow the caster to control the victim. I say victim, because it is against their will and is usually not desired by the one bound.
Trapping is drawing a spiritual entity into an object or vessel and keeping them there. It's known quite well in Arabian magick and legend. That's why djinn were trapped in vessels, to control them and keep them contained. I once trapped an evil entity that continued to come back despite banishment or exorcism of the house. I buried the jar, knowing fully well that when the jar broke the being would be freed, but hoping it would learn its lesson and leave my mother-in-law alone after its "time out" lol. So far so good, and it's been 6 years. I don't trap often because it is usually not necessary.
Banishment is merely sending away. You can banish spirits, negative energy, and even physical people. It doesn't mean they're trapped or bound. They're merely forced to leave you, the people, or the place you banish them from.
And for the sake of information, exorcism is driving out something by force.