Trust and faith are synonymous according the Merriam-Webster.
Entry Word: faith
Function: noun
Text: 1
Synonyms BELIEF 1, credence, credit
Contrasted Words dubiety, dubiosity, skepticism, uncertainty
2 Synonyms TRUST 1, confidence, dependence, hope, reliance, stock
Contrasted Words disbelief, incredulity, unbelief; apprehension, misgiving
3 Synonyms RELIGION 1, creed, cult, persuasion
4 Synonyms RELIGION 2, church, communion, connection, creed, cult, denomination, persuasion, sect
Related Word doctrines, dogmas, tenets