Faith is the realization of what is hoped for and evidence of things not seen. (Heb. 11:1)
If I buy I lottery ticket I hope I will win but I still plan on going to work in the morning. If I buy the ticket and then immediately quit my job then I have faith that I will win.
I do not recommend anyone actually do that, I am simply using a descriptive illustration.
Hope is mentioned as a virtue because we should always desire for justice, peace, everlasting life, etc… You can’t have faith until you first have hope.
Another area they differ is that hope tends to more generic, e.g. I hope there’s life after death. Faith fills in the specifics: there’s hosts of angels and saints in heaven giving glory to God. Its in this sense that the Epistle to the Hebrews is addressing.