Your first diagram shows the behavior of the motor alone. The feedback (back EMF) shown does exist, but it does nothing to stablize the motor speed against load changes. For a given voltage in, and a fixed load torque (bearing friction, load friction, air resistance, etc) you can set the motor speed by varying the input voltage. Some systems do this quite handily - electric fans, for instance. However, if you vary ("disturb") the load torque, the motor speed will change. This is not an issue for some applications (electric drills, electric golf carts, etc). For these applications, the operator supplies the feedback when the output speed needs to be constant.
Because there is no built-in stabilizing loop, these systems are called "open loop", although if you include the effects of a human operator this description is not accurate.
When you add external control paths, as shown in your second figure, the effects of the added tachometer allow the system to maintain speed without operator intervention, and these are called closed-loop systems.