WithTimeout vs WithDeadline: what is the difference, and what happens when a child asks for a later deadline than its parent?

WithTimeout(parent, d) is exactly WithDeadline(parent, time.Now().Add(d)). Use a timeout for a relative budget ("this call gets 2s") and a deadline when an absolute time is passed down from outside (for example a gRPC deadline or a job's SLA).

A child can never extend its parent's deadline. If the parent's deadline is already earlier, WithDeadline skips the timer and returns a plain WithCancel(parent). The child's Deadline() then reports the parent's earlier time.

parent, cancel := context.WithTimeout(context.Background(), 100*time.Millisecond)
defer cancel()

child, cancelChild := context.WithTimeout(parent, 10*time.Second)
defer cancelChild()

d, _ := child.Deadline()
fmt.Println(time.Until(d) <= 100*time.Millisecond) // true: the parent's deadline wins

Gotcha: if you really need work to outlive the parent's deadline (for example cleanup after a timed-out request), derive from context.WithoutCancel(parent) and set a new timeout. Deriving again from the original parent will not help.