Both are declarative rule engines on Lead/Case but they trigger at different times.
Assignment Rules fire on record create (and optionally on edit, if the user opts in via "Assign using active assignment rule"). They evaluate criteria top-down and route the record to the first matching entry. The action: change the Owner (to a user or queue), and optionally send an email notification.
Use Assignment Rules for: "When a Case is created with Severity = Critical, assign it to the Tier-3 queue and email the manager." Or "Lead from EMEA region routes to the EMEA queue, lead from APAC routes to the APAC queue, otherwise default queue."
Escalation Rules fire based on time elapsed without resolution. You define entry criteria (e.g., Status = Open AND Priority = High) and time triggers (e.g., 30 minutes after creation, 2 hours, 4 hours). At each trigger, you can change the Owner, change the Priority, or notify users. Escalation rules implement SLA workflows.
Use Escalation Rules for: "If a High-Priority Case is open for more than 30 minutes during business hours, reassign to a manager and email an alert. If still open at 2 hours, escalate to the executive team."
Key differences:
- Trigger: Assignment fires on create/edit; Escalation fires on elapsed time.
- Direction: Assignment is initial routing; Escalation is "this isn't being handled".
- Business Hours awareness: Escalation Rules can use Business Hours to pause the clock outside working time. Assignment Rules don't have this concept.
- Per-object support: Assignment Rules exist on Lead and Case. Escalation Rules exist only on Case.
Both can co-exist on the same object — Assignment routes new cases, Escalation chases stale ones.