With an approved developer account, you will be able to create and manage Twitter apps, which you will use to make requests to our APIs.
If you would like to make a request to an API on behalf of another user, ie post a Tweet for a different @handle, you will have to use the 3-legged oauth flow to receive the proper access tokens for that user that you will use in your request to the POST statuses/update endpoint along with your Twitter app’s consumer key and secret.