Long term target = what a control chooses to regulate
A control law utilizing integral feedback involves a choice of "regulated variable". This is the response parameter whose error (difference between command and response) the control law will drive to zero in steady state. With C* the regulated variable is a mix of pitch rate and normal load factor. With C*U a third parameter is added - speed deviation from a reference.
The Boeing C*U system adjusts pitch attitude (and thus flight path angle) such that, in steady state, speed will match the reference speed. In this way, C*U provides speed stability.
It is important not to confuse speed stability (pertaining to the pitch axis long mode or phugoid mode) and maneuver stability (pertaining to the short period mode). These modes are separated sufficiently in frequency (~.02 Hz vs. ~0.5 Hz) that they can be treated individually. Both the Boeing system using C*U and the Airbus system using C* alone provide augmentation to improve closed loop short period characteristics.
Also keep in mind that with control system feedback augmentation there is a difference between open loop stability and closed loop stability. With the feedback control system operational, the flight crew only experiences the closed loop stability. Allowing the open loop short period stability to be relaxed improves airplane fuel economy performance. Use of feedback control to provide desirable closed loop stability keeps the flight crew happy and reduces their workload.