Short Answer
A statement might be held to mean utterance, sentence, proposition, message, or speech. A premise is a statement that is used as a basis to draw an inference. Thus, a premise is a type of statement selected with the intention of reasoning to a conclusion.
Long Answer
In philosophical writing you will see "statement" used in several different ways:
- A statement might sometimes be held equivalent to an utterance, where the emphasis on not on the semantics or syntax but the physical encoding. Utterances might be something like "Yikes, save me!" uttered in surprise as an exclamation where the philosopher is emphasizing the non-cognitive aspects like the emotion of astonishment or the sound of the message moving through the medium of air.
- In the philosophy of language, a statement might be held the same as a linguistic sentence where the emphasis is on the syntax and closely related to a sentence in linguistics. Notice Noam Chomsky's example of a statement that is puzzling but somewhat comprehensible.
- It can be used as a truth-bearing compositional unit of meaning. In this sense, it is a synonym for proposition. Here the emphasis on semantics and the abstracted part of a communication. Propositions are important units in truth-conditional semantics.
- Sometimes, a statement needn't be expressed in a language, natural or otherwise at all. In the philosophy of law in the US, action can be taken as a statement or speech, such as in symbolic speech. This is closely related to implicature where there is a difference between the literal meaning and the pragmatic meaning. Often, the word message is used synonymously in this sense.
And premise? Generally just a statement that is used in reasoning to get to a conclusion.
P1. Socrates is in the kitchen.
P2. The kitchen is in the house.
C. Socrates is in the house.
In this example, the conclusion is not a premise, but is a statement.