The data plane is what actually moves traffic from one port to another. Learned routes from the control plane are programmed into the data plane. When traffic moves from one port to another, most of the time the control plane isn’t involved, unless it’s a special type of traffic, like IKE or ICMP. In a chassis-based system (like the above examples), these too are line cards that you can add or remove. There are a lot of different models here, and they support everything from copper connections at 1Gb and 10Gb, to fiber connections at 1Gb, 10Gb, 100Gb, and 400Gb. In a fixed-form device, such as a Juniper QFX-5110 or a Cisco Catalyst 3750, these are not removable. A hardware failure here usually necessitates replacing the entire device.
Think of the data plane as the workers in an assembly line. They don’t make decisions, their job is to just move things (packets) as quickly as possible.