Most of my grafting experience thus far has been with stem grafts, which involves fusing a piece of scion wood onto the existing tree or root stock. I’ve become pretty comfortable grafting apple, pear, quince, and plum trees this way. However, stone fruit like cherry and peach do better with bud grafting. In this case, grafting is performed in summer; and only a single bud with a sliver of bark is tucked into the bark of the host tree. The injury to the host tree is much smaller and heals over faster.
The success rate of bud grafting is generally higher and it is the preferred technique in commercial grafting. The downside is that you need to wait until the following year to see the bud begin to grow. I was dubious about this technique, but I’m happy to note that my bud grafts from last year are leafing out.
Here’s a nice example of an inverted T bud graft of plum on plum: