Translate light, inextensible and smooth assumptions into forces and motion constraints.
A connection constrains relative motion
Model
Consequence
Light string
Neglect its mass. A taut straight section has one tension magnitude.
Inextensible, taut string
Length is fixed; in a simple fixed-pulley system the particles have equal speed and acceleration magnitudes.
Smooth pulley
With a light string, tension has equal magnitude on the two sides.
Light rigid tow bar
Neglect its mass; it may pull in tension or push in compression.
Contact between load and platform
While contact is maintained, they share the relevant motion; the normal force pushes rather than pulls.
A string transmits tension only. If the forces required by an assumed taut-string model would compress it, the string becomes slack and that constraint ceases to apply.