In Juniper firewall filter configurations, "discard" and "accept" are two valid terminating actions for a term within a filter. The "discard" action drops the packet, preventing it from reaching its intended destination, while the "accept" action allows the packet to pass through the filter, proceeding to its next hop or destination. "Count" is a non-terminating action that increments a counter every time a packet matches the term but does not inherently determine the packet's fate. "Next term" directs the evaluation to proceed to the next term in the filter for further processing, also a non-terminating action.