A (rechargeable) battery uses a closed cell and a reversible chemical reaction to generate power. A + B -> C + Electricity, but also C + Electricity -> A + B. That way, you can “store” energy in the battery by forcing it to form A + B when you’re charging it. When the battery isn’t connected to anything, the electricity cannot dissipate easily, so it stays as A + B. Once you hook it up to something to use it, then the electricity dissipates and allows the A + B -> C + Electricity reaction to keep moving. The only inputs and outputs are electricity/power.
A generator outputs electricity using physical inputs, usually (we’ll deal with solar panels later). In the broadest sense, a generator uses physical motion to move a magnet around a coil of wire. The moving magnet changes the electromagnetic field around the wire, which induces a current in the wire. That current is electricity.
The source of physical motion for most generators is a steam turbine; burn fuel to heat water to steam to push against a turbine (fancy fan) which spins a shaft which is now physical motion for the generator. Other methods are wind and water; a windmill or watermill capture the energy in moving air or water to spin a shaft, generating physical motion for the generator.
A solar panel takes in light energy and puts out electricity. The solar panel is designed in such a way that electrons can be “kicked” from one side of the panel to another by light at a certain wavelength. This creates an imbalance of charges between the two sides; by connecting the two sides with wires, the electrons will try to fix this imbalance by moving. This movement of electrons generates (or is) electricity.
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