Pretty sure most of you already know this but for those who don't: you have two clipboards in Linux. One is the traditional clipboard where you copy with control c and paste with control v. The other one is when you highlight text and use the mouse middle click to paste text.
More details here.
If I understand it correctly, Wayland only specifies a single clipboard but no primary. But most (all?) wayland compositors implement an additional protocol that's also supported by the toolkits (gtk, qt, …) and programs like wl-clipboard.
So yes, wayland also has clipboard + primary. But no secondary, as far as I found. Though I never used secondary on X anyway.