Nope not exactly that it's the same as your Bolens.
First pic is a '68 12 Hp Tecumseh, second pic is a '77 16 overhead Tec like your ST12 motor. While similar, they are different.
Also, these motors use a Solid state ignition module. He is correct, they are expensive to buy the original ones, but do not fear, there are several alternatives out there for replacement. Your Bolens most likely uses the first gen module the Sears will us the 3 rd gen one
* For a direct replacement, check out Dale Colvert's Overnight Solutions ignition, it is a modern day direct bolt on.
* Ed Stoller has a website www.enginesandmagnets.com He explains the workings of the ignition system and he offers a new pickup sensor, you buy other parts that explains. His buddy Mike Brown sells a complete kit you can buy linked on his website. These systems convert ignition over to battery-auto coil.
* Brian Miller on garden tractor pulling tips also has a couple conversions, again these convert to battery ignition.
*My buddy designed another system for my tractor as I burnt up 2 modules in 1 month. Here is link to my write up.
68 SS 12 flat head 12 Hp Tecumseh
77 16 Hp Over head Tec