The word trust describes a psychological state. A person trusts something or someone. That is a decision inside that person's mind. This means that trust is not achievable by engineering. If you want to get someone to trust you, you need to become a con artist.
The word trustworthiness describes a state of a system. Trustworthiness can be achieved by proper security engineering. People can be trustworthy, in which case that trustworthiness is achieved by proper moral upbringing.
If a system is trusted, you don't know whether it is trustworthy or just had a good con artist selling it. If a system is trustworthy, then you know something about it.
Let us please start using these words in their proper contexts!