Ko rules are the rules with the primary, if not exclusive, purpose of restricting cycles. Other restriction rules related to passes or suicide have restricting cycles as a secondary effect.
The term ko is generally used to refer to basic ko (recapture of a single stone), but may also more generally be applied to any repetition.
The basic ko rule used in many older rule sets only forbids retaking simple kos. More recently, rules have been designed to prevent any cycle. These include:
Unless you’re a rules expert, there is little need to worry about all these different rules. For the normal ko situation all these rules are the same. All those more complicated situations are extremely rare, and if you ever have the idea that you are in one of them, just call in the referee, or a rules expert.