Distillation of diethyl ether and tetrahydrofuran
Sodium and potassium are both drying agents. Being alkali metals they react (often vigorously) with water. 

Sodium wire is often used in diethyl ether stills, whilst potassium is used in tetrahydrofuran stills. In general, potassium is more reactive, and hence a better drying agent.

The reason different desiccants are used is due to temperature. THF boils at a higher temperature, meaning a lump of potassium metal can be used in the still ( the lump of K melts once the THF reaches reflux ). Diethyl ether boils much lower, meaning potassium would not melt, for this reason sodium is often used in the form of a wire (giving a much larger surface area). 

In respect to the use of benzophenone (or other indicators such), it generally indicates the presence (or absence) of oxygen in the solution. In the past, it was thought that the purple (blue is actually not great) colour was related to the moisture content, however we now know that the colour is related to the oxygen content. For this reason, using the indicator allows us to determine how oxygen-free the solvent is. A purple THF/ether still in which metal is still present indicates that the solvent is both dry and oxygen free,