Rules are traditionally referred to along a spectrum, where on one end they are open and the other they are closed. While there is wide variation in the middle, there are certain standard kinds of rules.
Open Rules—permit the offering of any amendment that otherwise complies with House rules, and allows debate under the 5-minute rule.
Modified-Open Rules—operate much like an open rule, but have some restriction on the “universe” of amendments, either through a pre-printing requirement or an overall time limit on consideration of amendments.
Structured Rules—specify that only certain amendments may be considered and specify the time for debate.
Closed Rules—effectively eliminate the opportunity to consider amendments, other than those reported by the committee reporting the bill.