Cleft heal in half the time normally of a bark graft and the union is typically stronger. If the callery was 6" a bark graft is the better choice. If the trunk can be easily split with a butcher knife the cleft pinches the scion holding the graft together and makes a great union. For those in Europe and other parts of the world they are referring to a rind graft aka bark graft. A cleft will likely close in the first year or two. There are rinds I’ve done on large trees that were still closing 5 or 6 years later. Will take some photos for you of clefts as they heal the difference can be shocking. Here is an older thread where I ask Mark about the problem I’m bringing up Cherry budding issue
Here is a cleft graft of mine healing and its ugly but closed quickly.
Here are rind grafts of mine healing. That bottom picture was a rind graft still not closed after years.
The rind looks like a big blob on top of the tree stump.