If you’re using a public board, the participants don’t need to have an account because with public boards anyone that has the URL can have access to the board.
The participants who join a public board they’ll join as anonymous users without the necessity to create an account, they’ll also be able to create cards and vote.
If you’re using a team board only people that you invite to your team will have access to it. In order to invite people to join your team and to access the team board they’ll need to have an account.
If you want to know more detailed information about the difference between a public board and a team board, click here.