Seltzer and carbonated water are the same thing. Club soda is slightly different. "Seltzer" comes from German:
The term seltzer water is a genericized trademark that derives from
the German town Selters, which is renowned for its mineral springs.
Naturally carbonated water has been commercially bottled and shipped
from this town since the 18th century or earlier. Generally, seltzer
water has no added sodium salts, while club soda still retains the
So, the primary difference is that seltzer has no added ingredients, but club soda does:
Sodium bicarbonate, sodium chloride, sodium phosphate and sodium
citrate are added to club soda…
Here's a decent review of the ingredients list and taste of various types of fizzy water.
So to answer your question directly, you can make seltzer just by carbonating regular tap water, and you can make club soda by adding potassium bicarbonate, potassium sulfate, or baking soda to water and carbonating it.