For tool holders, there are screw type, ie hole in the middle of the insert. These same inserts generally also have various top clamp options. Some use the same hole insert, but have a centre pin that pivots in such a way that it retains the insert, while others may have a wedge design that then pushes the insert to a centre pin to hold it. There is also the top clamp that does not require a centre hole, and some holders will take both inserts of the same geometry, but with or without the centre hole. Where possible, I try and buy the top clamp style holders that take the common inserts with a centre hole. An outer turning tool insert can then be used in a boring bar if it takes that geometry insert, (usually a N neutral geometry insert) and the boring bars, especially the smaller ones under Ø20mm have a centre screw for the inserts anyway. Some brands will go down to 8mm shanks for the outer turning tools, but most are the 3/8(9.5mm) or the 10mm shank tools. Some tools like the TNMG16 holders often start at a 12mm shank, so need thinning on the bottom side to bring the insert to the holders centre line height, in my case 9.5 mm for my Myford S7. The smaller CCMT 06 inserts, are available in 8mm shanks. I try and stay with common industry standard insert sizes and get my holders to match best as possible, and only thin if I have too. You can tell the common industry standard by getting a book from a company that sells locally. The common ones have loads of geometry styles as well as material grades and coatings. The less common only have a few geometry styles , and often only offer the inserts in a few grades , sometimes with no other coating options. I learnt long ago that a cheap insert is not always cheap in the longer term. Most of the tooling company catalogues these days are a wealth of information, with optimised cutting conditions and what coatings etc can do what. If you do interrupted cutting, they have insert suggestions and grades for that as well.
The book is well worth having a look at to see what is happening.
Neil