You are only allowed (4) primary partitions. The "and" does not apply.

One of my beefs is manufactures that use up that allotment i.e. windows
recovery, windows, special manufacturer tools, and I think backup,
without placing some of this in an extended partition. Extended
partitions can be used for more partitions, I have put more than 4
partitions on an extended partition, this makes more than eight total.

Only way to add partitions is with labels, without them it is
unmanageable so be sure to label your partitions.