These two systems are deeply interconnected. The engine produces power; the transmission converts and delivers it. When one struggles, it stresses the other. An engine running rough delivers inconsistent torque pulses to the transmission, accelerating wear on clutch packs and bands. A transmission that's slipping forces the engine to rev higher to maintain speed, which increases heat throughout the drivetrain. Problems that start in one system frequently create symptoms in the other.
This is why we often see customers who've been told they have a transmission problem when the real root cause is an engine issue — or vice versa. A full diagnostic looks at both systems together, not in isolation.