A trustless system eliminates the need for participants to know or trust each other for the system to work. Trustlessness means no central figure (like a bank) has authority or control over the said system.
Bitcoin is trustless because Bob can send Tina 1 Bitcoin without the need for a financial intermediary to oversee the transaction. Bob can use the blockchain to be certain the transaction is valid, eliminating the need to “Trust” Tina or an intermediary.
A permissionless system lets anyone participate and does not require an application and approval from a central authority, like a bank, to use the services on the blockchain. Permissionless systems are synonymous with the ideas of transparency, decentralization, and accessibility. Bitcoin and Ethereum are the best-known examples of permissionless blockchains.