What is the difference in the making of yoghurt to produce carbonated (like Kefir) vs non-carbonated yoghurt?
There are different kinds of lactic acid fermentation which are done by different kinds of bacteria and/or yeasts. 

The simplistic picture is that yogurt is typically made with only two types of bacteria (lactobacillus bulgaricus and streptococcus thermophilus) that perform only homolactic fermentation converting sugar (glucose) into lactate only. In contrast, Kefir is made with a larger mix of bacterias that perform homolactic fermentation as well as heterolactic fermentation, which converts glucose into carbon dioxide (CO2), ethanol and lactate.

For this reason, kefir is carbonated and have even slightly alcoholic.