Performance textbooks classify prop vs. jet based on whether the propulsion system is considered 'thrust producing' or 'power producing'.
Whether a propulsor is thrust or power producing is based on two factors.
Is the thrust (or power) available roughly constant with velocity?
Is the fuel consumption roughly proportional to thrust (or power)?
An idealized jet is a thrust producing engine. The textbook assumptions say that a jet's thrust available is constant with velocity and the fuel consumption is $\dot{W}=\mathrm{TSFC}\,F_n$, where $\mathrm{TSFC}$ is the thrust specific fuel consumption.
An idealized prop is a power producing engine. The textbook assumptions say that a prop's power available is constant with velocity and the fuel consumption is $\dot{W}=\mathrm{BSFC}\,P_{shaft}$, where $\mathrm{BSFC}$ is the brake power specific fuel consumption.
In reality, these idealizations are never true. Serious aircraft performance modeling requires a more sophisticated propulsion model and these concepts of 'thrust producing' and 'power producing' are not very useful. The approximations that result (such as best climb, endurance, range -- at best CL/CD, CL^1/2/CD, or CL^3/2/CD) are not very accurate. Similarly for the Breguet Range equations for prop and jet aircraft. Unfortunately, most of the textbooks that present these approximations never discuss the reality of propulsion and the deficiencies required to write these simplifications.
The design of a duct for a fan has profound impact on the performance of the fan. High speed aircraft (cruising at M=0.8 and above) will have a duct shaped such that when the flow reaches the fan front face, it is substantially slower than freestream (say M=0.6). This helps keep the fan tip speed down and allows the engine to operate at high speeds. This kind of fan actually reduces static thrust. These ducts typically have an exit area smaller than the fan area.
Ducts can also be designed to maximize static thrust. These fans actually accelerate the flow from freestream to the fan face. Though they are unsuitable for high speed flight, they are great at static thrust. These ducts typically have an exit area equal to or greater than the fan area.
Duct performance behavior also depends on how you're driving it -- a gas turbine, a piston engine, or an electric motor. And how the limits on that device are enforced. For example, an electric motor and drive will have certain RPM (bus voltage and throttle) and torque limits (current).
In a sophisticated system, these will be monitored and kept within safe limits by an active control system. In a hobby-grade system, the battery bus voltage drops without control, the speed controller has a 100% throttle, and the controller may limit current -- or perhaps a fuse is the only limit you have. Sometimes, the only limit is by choosing a prop that won't overload or allow the system to over-speed.
My recommendation is to take a step deeper in your calculations and develop an off-design engine deck for your propulsor.
If you are designing a high-speed fan like that used on a transport aircraft, you will start with a traditional turbomachinery fan map.
If you are designing a low-speed fan that will not operate into compressibility, then I would recommend you use Prof. Drela's DFDC. Esotec is a company that claims to have an improved version.
Next, you are going to need a model of the device producing shaft power -- turbine, piston, or electric. Importantly, what are the limits -- max torque, max power, max speed -- these will form an envelope of what is allowed. Ideally, you will also have some measure of efficiency or fuel consumption within those limits.
Finally, you need to couple the two together -- match the torque and speed required to spin the propulsor with the operating torque and speed of the driving machine. Keep the machine within safe operating limits, move the propulsor around in the flight envelope (speed, altitude, throttle).
This paper gives an example of this for a high speed fan driven by an electric motor.
