In the academic world there is often confusion about the concept of trust. Or better the same world “trust” has two different meanings. From now on, I’ll try to use (and push) these 2 different words for the 2 different concepts: Soft Trust and Hard Trust.

Hard trust refers to authentication of resources and has to do with digital signature and public key cryptography.
Soft Trust refers to interpersonal relationships.

Hard Trust is involved in “I trust the person who phoned/mailed me was Alice”. It means I’m certain about her identity.
Soft Trust is involved in “I trust Alice to help me when I’m in trouble” or “I trust the judgements of Alice about movies”. It involves a much more human sense.

Ok, these definitions are not very precise I agree. You can help me by editing them on the Trust metrics Wiki: Soft Trust, Hard Trust.

I think this concept are well explained in the introduction of Trust Networks on the Semantic.
“Trust” is a word that has come to have several very specific definitions on the Semantic Web. Much research has focused on authentication of resources, including work on digital signatures and public keys. Confidence in the source or author of a document is important, but trust, in this sense, ignores many important points. Just because a person can confirm the source of documents does not have any explicit implication about trusting the content of those documents. This project addresses trust as credibility or reliability in a much more human sense. It opens up the door for questions like how much credence should I give to what this person says about a given topic, and based on what my friends say, how much should I trust this new person?”