Tilt means to move something in such a way that it is on a slant, slope, or incline relative to the ground. If something is tilted, it is at such an angle already.
Ex: If you tilt the container and pour some of the water out, it will be much easier to move, I'll bet. Water is much heavier than most people realize.
Ex: My garden gate has been hit by cars so many times that it is battered, the door hangs from one of its hinges, and it is so tilted that it scrapes on the floor when you try to open it.
Tilt also has many metaphorical meanings. If you are moving at top speed, we say that you are going full tilt. When someone is tilting at windmills, he or she is fighting imaginary enemies.
Ex: In the last fifty yards of the race, Bill turned up his speed. He came around the last turn going full tilt, and he managed to just edge out the leader at the tape to win the race.
Ex: My friend Tom is always convinced that everyone is out to get him. No matter how many times I tell him that he is paranoid or that he is tilting at windmills, he persists. Some people never change.
Literally, to lean is to incline or deviate from a vertical position towards a horizontal one. Figuratively, leaning can mean an inclination in feelings or desire.
Ex: The Leaning Tower of Pisa is called that because it leans at about 4 degrees off a fully vertical position. This happened because of a poorly built foundation.
Ex: I asked the principal who she had decided to give the job to, and she told me that she was leaning towards giving it to the veteran teacher who had applied, because he had more experience.
If something is leaning against something else, it is resting against it and being supported by it. This meaning also carries over into the figurative sense, in which leaning on someone can mean looking to that person for support and strength.
Ex: I have left the snow shovel outside. I have left it leaning it against the side of the house so that it can't get buried in snow if more falls, although of course, I hope that no more snow falls.
Ex: During the hardest times, I've really been leaning on my wife, because she is a tower of strength and optimism. She can get me through anything with her attitude.