When your context fills up, /clear is the default. Run it, then open the new session with a focused catch-up prompt: 'Here's where we left off and what I need next.' You control exactly what Claude knows going into the fresh context.
/compact is the fallback for when you're deep in a session and restarting means re-explaining hours of accumulated context. It summarizes the conversation and continues from that summary. You lose the exact wording of earlier messages, the full content of files read, and tool outputs not directly relevant to the current task. I reach for it only after + exchanges on a single complex problem, when a clean restart would cost more than it saves.