Isn't an offer always a suggestion?

Student or Learner
"Do you want to listen to the radio ?" Is this an offer or a suggestion or maybe both ?
Isn't an offer always a suggestion?
Yes, if we don't think of other meanings of the word "offer". But I think that a suggestion is not always an offer. Somebody asks:"Do you want to listen to the radio?". If she/he is willing to help you find a radio or lend you her/his radio then I would consider it an offer. But if she says afterward:"Then let's go to pub and listen to the radio!" then it would not be an offer in my opinion.
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