Como é que se diz isto em Inglês (EUA)? comunicate a message in phrasal verbs? is it get across a message or put across a message? do they mean the same?

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Get across or put forth. Get across means that you communicated the message in a way that people were able to understand it. Put forth just means to state the message.

I want to get across the message that we will help as many people as we can (I want to make sure people understand that we will help as many people as we can)

I want to put forth the message that we will help as many people as we can (I want to state publicly that we will help as many people as we can)

Put forth is more about putting the message out there in the world. However, the message might not come across right - people might misinterpret it. If they understood the message the way you wanted them to, then you got the message across.