The "bright edge bokeh" is a result of overcorrected spherical aberration. It's very common in the foreground blur from long telephoto lenses, since these tent t be designed for smooth blurry backgrounds.

"Bright center" is undercorrected spherical aberration. Often introduced on purpose, for extra smooth backgrounds - see above.

"Donut" is what you get from catadioptric (mirror) lenses.

Here's an example of different foreground and background bokeh, foreground on the left and background on the right in this example. Just having fun with swings, and a big fast lens: 300mm f:4.5 Xenar, at f:4.5 on 5x7" film: