notation - How are lowercase k and uppercase K used in general chemistry courses?

Where do lowercase k and uppercase K make appearances in general chemistry, and what do they signify?

Answer

In addition to the original answer I also allowed myself to invite lowercase Greek letter kappa κ to the table as typographically it has a similar-looking appearance and add some more definitions:

Lowercase k

Uppercase K

Lowercase Greek letter kappa κ

Uppercase Greek letter kappa Κ

Both lowercase k and lowercase Greek letter kappa κ

Both lowercase k and uppercase K

• $k$ and $K$ is in general may refer to a coefficient (German "Koeffizient"); indices are often used to denote which one, e.g. mass transfer coefficient $k_\mathrm{d}$, octanol/water partition coefficient $K_\mathrm{ow}$.