A book rests on a table. Two forces act on the book: the Earth's downward gravitational force and the table's upward normal force.
They are equal in magnitude and opposite in direction. That sounds exactly like a third-law pair. It is not one.
Equal and opposite is not enough. One question separates a third-law pair from two balanced forces on one object: count the objects the forces act on.
The two forces of a third-law pair act on two different objects, one force on each.
Two balanced forces act on one and the same object.
Run the test on the resting book. The weight acts on the book. The normal force also acts on the book. Both forces act on one object, so they are balanced forces on the book, not a third-law pair, however equal and opposite they are.
A third-law pair also keeps one type across one interaction. The book's weight is gravitational and the table's normal force is a contact force: two different interactions, a second sign that they are not partners.
The normal force's true partner is the book's downward contact force on the table. The weight's true partner is the book's upward gravitational force on the Earth.
So the sort runs on one question: do the two forces act on one object, or on two? One object: balanced forces. Two objects, one force each way, inside one interaction: a third-law pair.
A hanging plant is held by a cord. The cord's upward tension force on the plant and the Earth's downward gravitational force on the plant are equal in magnitude. Are they a third-law pair, or balanced forces?
Count the objects the two forces act on.
The tension acts on the plant. The gravitational force also acts on the plant.
Both act on one object.
They are two balanced forces on the plant, not a third-law pair.
Imre and Beth stand on ice. Imre exerts a force on Beth, and Beth exerts a force on Imre, equal in magnitude and opposite in direction. Are these a third-law pair, or balanced forces?
Count the objects the two forces act on.
One force acts on Beth. The other acts on Imre.
Two objects, one force each, inside one interaction.
They are a third-law pair.
A mallet exerts a force on a fence post, and the post exerts a force on the mallet. Which description fits these two forces?
A road exerts a forward force on a car's tire, and the tire exerts a backward force on the road. Which description fits these two forces?
A ceiling lamp hangs still. The cord's upward tension force on the lamp and the Earth's downward gravitational force on the lamp are equal in magnitude. Which description fits these two forces?
A parked car sits on level ground. The ground's upward normal force on the car and the Earth's downward gravitational force on the car are equal in magnitude. Which description fits these two forces?
A magnet exerts a force on a refrigerator door, and the door exerts a force on the magnet. Which description fits these two forces?
A swimmer floats without moving. The water's upward force on the swimmer and the Earth's downward gravitational force on the swimmer are equal in magnitude. Which description fits these two forces?
A mug rests on a desk. The desk's upward normal force on the mug and the Earth's downward gravitational force on the mug are equal in magnitude and opposite in direction. Why are they not a third-law pair?
A climber hangs from a rope. Which two forces are a third-law pair?
Two forces are equal in magnitude and opposite in direction. Which extra fact would show, on its own, that they are NOT a third-law pair?