The sensory and motor pathways can indeed be considered separately both in concept and physically. Of course the nervous systems is a single network of neurons, but that doesn't stop it from having separate components.
One can indeed often simplify neural pathways as "IN (sensory) ===> (black box with decision-making magic) ===> OUT (motor)"
Reflex arcs are a great way of demonstrating this separation because they do not involve the more complicated integration of the brain. Let's take the knee-bend (patellar) reflex as an example: https://en.wikipedia.org/wiki/Patellar_reflex
The diagram is correct in concept but let me add the anatomical detail to illustrate how sensory and motor pathways are separate, yet connected: When the reflex is triggered, the signal travels up from the sensory neuron ends located under the knee cap (these are dendrites) to the sensory neuron's body in the spinal chord. The sensory cell relays the signal via its axon, which then synapses with a motor neuron's body also in the spinal chord. The motor neuron then sends a motor impulse via its axon back down to the leg, where it triggers muscle contraction.
Physically, in this case there will be a separation also in nerves (at least if I may trust Wikipedia for now), where the sensory reflex neurons' dendrites travel from the leg to the spinal chord through an afferent nerve and the motor neurons' axons travel in the reverse direction through an efferent nerve. The only physical and conceptual connection between the sensory pathway and the motor pathway is the synapse between the sensory and the motor neurons in the spinal chord.
More complex sensorimotor pathways might include interneurons or integration with various circuits in the brain, but it is usually possible to define discreet separate parts of the pathway, one sensory and one motor, with the only connection being those interneurons.
Sensory and motor separation in the CNS
The central nervous system (CNS, which includes the brain and the spinal chord) is actually surprisingly organised in this regard, with quite strict separation of motor and sensory pathway components. For example, the cortex of the brain has distinct regions which contain sensory neurons for evaluation of various types of peripheral skin sensation. Separate from these are regions which contain motor neurons for movement of skeletal (voluntary-control) muscle. The interaction of these is of course more complex given that it involves skin sensation and conscious decision making in regards to movement.
Likewise, the spinal chord is structured into sensory and motor regions. In summary, the spinal chord consists of: 1) cell bodies (motor, sensory, inter; grey in the picture), 2) ascending axons (blue), 3) descending axons (red). Similar to nerves, axons going up or down the spinal chord are bundled into "tracts". Sensory axons are never bundled with motor axons, making it possible to create a map of the spinal chord in cross-section.
The tracts' names might be a bit confusing at first, but on second look are actually pretty self-explanatory. They usually contain where the axons come from and where they are going in order to synapse with other neurons. E.g. the spinocerebellar tract is formed of axons coming from the spine and going to the cerebellum. Given that the cerebellum is near the brain and the spine is further down, this is obviously an ascending tract - and ascending tracts are always sensory (because sensory information never needs to be carried downwards due to the brain being at the top).
Where it gets blurry
The sensory/motor separation isn't always as clear as I've described above. In fact, nerves (bundles of axons anywhere in the body outside of the CNS) will usually contain both sensory and motor pipelines. In particular, the cranial nerves (12 of the most important nerves) all include sensory and motor components for the respective part of the body that they manage. E.g. the facial nerve contains both the sensory connections for parts of the tongue and the motor connections that control facial muscles.
Another more complex example is pain sensation, where interneurons in the spinal chord can feed back onto sensory neurons and inhibit their signals, or axons can inhibit those packed in the same nerve bundle simply due to electrical effects.