The word Onsen (温泉) can have the following meanings:
Onsens (including Kósens) are classified to 4 types according to the temperature at the gushing point of the spring.
Cool spring (冷鉱泉 in Japanese).
Precisely this is classified as Kósen, while the others are classified as Onsen.
Warm spring (低温泉 in Japanese).
Hot spring (温泉泉 in Japanese).
Extra hot spring (高温泉 in Japanese).
Conventionally, many onsen providers heat up the water or add cold water to adjust the temperature to approx. 41°C (105.8°F) which is the average temperature of Japanese bath.
Onsens are classified to 10 types depending on dissolved substances (mineral depositions), the types are defined by the Japanese onsen law. See the following descriptions for details:
Does not contain enough amount of minerals to be classified as one of the others.
The main component is carbon dioxide (CO2).
The main component is bicarbonate (HCO3).
The main component is chloride (Cl).
Contains iodine. This type is newly defined in 2014.
The main component is sulphate (SO4).
The main component is iron (Fe).
The main component is sulphur (S).
Acidic water. See the "pH" section in this page for details.
The main component is radon (Rn).
Onsens are also classified to 6 types according to the pH value.