newtonian mechanics - Why are work and energy considered different in physics when the units are the same?

There is a question that explains work and energy on stack exchange but I did not see this aspect of my problem. Please just point me to my error and to the correct answer that I missed.

What I am asking is this: Why in physics when the units are the same that does not necessarily mean you have the same thing.? Let me explain. Please let me use m for meter, sec= second , and kg = kilogram as the units for brevity sake.

The units for work are kg * m/sec^2 * m. The units for kinetic energy are kg* (m/sec)^2. They look that same to me. I need them to be the same so I can figure out the principle of least action. Comments are welcome.

Answer

One definition of work is "a change in energy." Any change in a physical quantity must have the same units as that quantity.

Different kinds of work are associated with different kinds of energy: conservative work is associated with potential energy, non-conservative work with mechanical energy, and total work with kinetic energy. In fact, that's one way to see the oft-quoted Law of Conservation of Energy:

$$ W_{total}=W_{non-conservative}+W_{conservative}\\ \Delta KE=\Delta E - \Delta PE \\ \therefore \Delta E=\Delta KE + \Delta PE $$

So just like impulse (which is a change in momentum) has the same units as momentum, work has the same units as energy. Any change in a physical quantity must have the same units as that quantity. A change in velocity has units of velocity, etc.

A more difficult question might be why torque has the same units as energy. This is more subtle, but the key concept is this: units are not the only thing that determines a quantity's interpretation. Context matters too. Energy and torque may have the same units, but they are very different things and would never be confused for one another because they appear in very different contexts.

One cannot blindly look at the units of a quantity and know what is being discussed. A dimensionful quantity might be meaningless or meaningful depending on the context, and it's meaning can change with that context. Action times speed divided by length has the same units as energy but without any meaningful interpretation (as far as I'm aware).