The difference between 'global' and 'globally' could be compared to the two different meanings of 'world'. "The world" in one context can refer to the planet earth, but in another context it could just refer to the people in it, the way they are organised, the populated world etc.
Likewise, 'global' generally means that something concerns all parts of the world, or at least a considerable proportion of it. 'Globally' generally means that something encompasses the entire planet, or includes all things.
'Global leading' seems correct to me, as it is not as all-encompassing as 'globally'. It allows for exceptions. For example, a particular smartphone manufacturer might be described as a global leader, yet there may be one or more specific markets where they are not. To say they are leading 'globally' would sound like an exaggeration.
On a side note, 'global leading' is one of those phrases that has been overused to the point that even the people saying it don't really know what it means. Mostly, you'll hear organisations described as 'global leaders', which means that they are leading the way for their peers on a global scale. You also hear of research or technology being 'global-leading' if it is shaping what others are doing, following the research or imitating the tech. It seems a little odd to me to describe a specific product as 'global-leading'. I think many get confused with the term 'leading', which in the context of products just means that it is a top seller - it is leading in terms of number of sales. As you probably know, technology that is truly 'global leading' does not always lead the way in sales. Cutting-edge tech is often too expensive for most people who wait for other manufacturers to be led by it and produce more affordable equivalents.