HAZ means which is affected by heat only (i.e. only at a range of temperature). So the HAZ characteristics should be same both at shoulder edge and the pin edge. But TMAZ i.e. thermo-mechanically affected zone which is affected by both the temperature and mechanical deformation which can be different in two different positions i.e. at shoulder edge and the pin edge. Because the application and magnitude of loads are different in that zones so the micro-structure can be varied.

The HAZ should be affected by the temperature field and thermal cycle. So I think the HAZ's position will be different if the "flow" of metal is different. Of cource, the heat in FSW is caused by the stir and friction between shoulder, pin and metal.  

Yes. It you have the sample, you can make the Metallographic  to certify it.  In general, the microstructure with the cross section of the joint is different . For example, the grain size, the orientation of the grain and the flaws.

I think more heat transfer by the surface during FSW and more width in HAZ than cross section area

Yes, the positions are different. The spread from the edge of the TMAZ (in terms of dimension) are usually in the same range  depending on the tool geometry and configuration. (Please note that heat generation is usually more from the tool shoulder). However, the HAZ at the top surface is farther away from the weld axis compared with the bottom. This means that when you look through the cross section of the weld, the distance between the HAZ and the weld axis reduces or tapers as you move from the top to the bottom of the weld.

Examine the HAZ of the AA6082-T6 alloy in the attached image

thank you very much...Pankaj Biswas, Qiyue Wang,Yongjuan Jing, Ahmed Al-Roubaiy and Uyime Donatus for your valuable answers