You "catch" something that is coming toward you, usually because someone threw it to you on purpose: A ball or another object. In slang, you might also "catch" a cold or other illness, which means you became sick, and if you understood someone, you "caught the meaning." You "grab" something that you want to take or hold, often when it does not belong to you or if you are trying to do it quickly. For example, you would grab your child's shirt if she tried to run into the street with out looking. Children often grab toys that other children are playing with. In slang, you might also "grab" a meal with your friends. They are similar because they are both actions that involve obtaining an object or something you can hold, but they do not mean the same thing. Grab has a slightly negative context; it is rude to grab things from people because it means you took it quickly without waiting for them to give it to you. If you catch something, it is already coming toward you.

They can be the same in some situations: grab a taxi/ catch a taxi. But: In the physical/sporting sense, CATCH implies something that was in motion: Catch a ball. GRAB usually does not have this sense. In informal use, they often are very similar: "Let's catch/grab a bite to eat" both mean to stop briefly to have a quick meal.