The way I gather, a explorative study is merely trying to identify certain concepts, whereas a explanatory study is trying to explain a A causes B relationship.
Especially with regard to case study research, Yin (book on case studies, 2014), mentions the following:
'For instance, many descriptive case studies deal with the “how” of a situation, whereas many explanatory case studies deal with the “why” of situations.'
But the way I see it, questions with regard to a 'how' situation are often explanatory in nature:
How does using an umbrella influence your sogginess?
How does e-commerce influence internationalisation process?
How does smoking influence heart disease?
Are these questions not explanatory in nature?