A transaction - UTXO’s, new output(s), input(s) and previous output(s).

[odolvlobo]

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An output's script typically contains an address.
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The output in the transaction just contains that resulting locking script, not the "address". Blockchain explorers and wallet software can recognize the script type and then rebuild the "address" from the available script data when displaying the transaction to humans, but that address isn't actually stored in it's address form anywhere in the blockchain.

My statement that an output typically contains an address was clumsy.

[BlackHatCoiner]

Hmm, I don't know how I should word this, nor would I say that I fully understand what you mean, could you expand on this?

Spending an output doesn't necessarily require a signature. What it does require is an unlocking script, which contains a signature 99.9% of the time, but not always. An example is the unlocking script for each address in this thread: REWARD offered for hash collisions for SHA1, SHA256, RIPEMD160 and other. To spend from address - 35Snmmy3uhaer2gTboc81ayCip4m9DT4ko - you "only" need to find an SHA256 collision; if you do, you can construct an unlocking script and claim the reward, i.e. spend the input without a signature.