Are energy and work the same thing? When revising formulas the other day I came across something:

Energy = power × time

If we substitute power we get

Energy = work/time × time

The time cancels out. So is work equal to energy?
 A: Work is close to being energy. Notice that both have the same units, Joules. Now, specifically speaking, work is the amount of energy transferred to an object through a force over a distance.
$$\text{Work} = F\cdot d\cdot\cos\theta$$
where $F =$ force applied to object, $d =$ displacement which object undergoes and $\theta$ is the angle between force and displacement vectors.
Note that what you get from algebra does not always reflect what you get in theory.
A: 
Are energy and work the same thing

No.
Work is one of the two means for transferring energy. The other is heat. But work (and heat) are not the energy itself. They are processes for transferring energy.
The energy transferred by work or heat results in an increase or decrease in the internal energy of the entities that  transfer the energy between them.
Hope this helps.
A: Yes and no, depending on what we are talking about.
Statistical physics
E.g., in statistical physics we will refer to work and heat as the means of changing the internal energy of the system $$dU=dQ -dA$$ Clearly, here work is the change of energy. Moreover, it is not the full change, if the heat transfer is also present.
Mechanics
In mechanics work is the product of the force and displacement $\mathbf{F}\cdot\mathbf{d}$. This does not necessarily change the energy of the system, since there may be another force doing the opposite work. In other cases it may transform energy from one form to another (e.g., kinetic energy into potential and vice versa). Finally, in non-conservative systems, it may indeed change the total energy, as in the case of friction.
Potential energy is work
Finally, it is not uncommon to encounter statements such as

potential energy is work required to assemble the system (or bring a charge from infinitely far)

Note that this still could be interpreted as a change in the potential energy.
A: Work is a transfer of energy. So they are closely related (including the same units) but they are not the same.
A: Work as well as heat are means of energy transfer. While you may have (or carry og contain) energy, e.g. thermal energy or kinetic energy etc., you can't "have" work nor heat.

*

*Heat is what we call thermodynamic energy transfer (miniscule vibrations passed on from particle to particle).

*Work is what we call mechanical energy transfer (larger displacements or volume changes due to mechanical forces).

So, saying that "work is energy" sounds slightly off in engineering ears. Rather, work is specifically "energy in transit", so to say.
Power is a term invented for energy-transferred-per-time. This could pop up in many scenarios. When you heat up water for spaghetti cooking, the transferred energy is heat, so the power might be defined as heat-per-time, $$P=\frac Qt.$$ When you run a car engine where pistons within the engine chambers compress and extend fuel gas, then the power might more usefully be defined as work-per-time, $$P=\frac Wt.$$ Bottom line, I usually always just write power as: $$P=\frac Et$$ (or possibly as $P=\Delta E/t$ to indicate that we are dealing with a change in energy) before I know which scenario to apply it to and which energy-transfer mechanism that is involved. Then your small equation rearrangement would simply be:
$$\text{energy}=\text{power}\cdot\text{time}=\frac{\text{energy}}{\text{time}}\cdot \text{time}\quad\Leftrightarrow \\ \text{energy}=\text{energy}.$$
A: 
Energy = power × time

No, it's not. The correct statement (assuming constant power or "the average" power) would be:

Energy change during a time period = power × time

Your other substitution is only correct if you are considering a process where the energy is only changed by work. In such processes it is indeed accurate to do that substitution and say:

Energy change = work

But in general the energy could also be changed via heat, so it's

Energy change (of a system) = work (done on the system) + heat (supplied to the system)

And that's the first law of thermodynamics. The clarifications in parentheses are crucial because they change the sign of the term. E.g. work done on the system increses it's energy, but if you'd consider work done by the system, it would spend and thus decrease the system's energy.
A: Energy is the capability of a body to make work, determined by the state of the body.
For example, a ball on the top of a tower can make work falling down by its position in the gravitational field of the Earth (potential energy). A bullet can penetrate a tree by its kinematic state (kinematic energy).
Generally, the energy type tells about which particular aspect of the body state confers energy to the body.
Energy and work share the same physical dimensions but they are not the same thing.
A: No, it's not the same. You need to perform Work to change Energy.
Eg. You need to lift a 10 kg object 2 metres from the ground:
Potential Energy of object at Ground Level = m x g x h = 10 kg x 9.81 x 0m = 0J
Work performed = Force x distance = 10kg x 9.81 x 2m = 98.1N x 2m = 196.2 N.m
Potential Energy of object at 2m above Ground Level = 10 kg x 9.81 x 2m = 196.2 J
A: Energy is something a physical system has; work is something done to or done by physical systems.
A: 
Work-energy theorem
The work-energy theorem explains the idea that the net work - the total work done by all the forces combined - done on an object is equal to the change in the kinetic energy of the object.

Here's a simple example that I think is useful for the basic concept of this relationship:
Imagine you have a 1kg weight and you carry it up a hill to a height of 100 meters.
We can calculate that the gravitational potential energy of the the weight has increased by 980J.  Q: Where did that increase come from?  A: When you carried it up the hill you did at least 980J of work.  In order to do that, you must have used (at least) 980J of energy.  I like to think (simplified and informally) of work as the application of energy.
A: 
This image represent how we earn money and spend also.
With physical example we understand better than a theoretical example.
Money is like energy we earn this by work . Work and energy has same unit but how different is clearly shown in figure .
Work is just a way to transfer energy , as work is just a way to get money and transfer this to get things.
