If you put a feeling or disagreement aside, you forget about it or ignore it in order to solve a problem or argument. We should put aside our differences and discuss the things we have in common We admitted that the attraction was there, but decided that we would put the feelings aside. = forget about
If you put something aside, you keep it to be dealt with or used at a later time. She took up a slice of bread, broke it nervously, then put it aside Encourage children to put aside some of their pocket-money to buy Christmas presents