Use ‘consequently’ when one event or idea is a consequence of another, meaning that the first thing led to the second. For example:
- I asked Campbell to edit my thesis; consequently, it passed without amendments.
- Great Britain declared war on Germany as a consequence of the latter’s invasion of Poland.
Use ‘subsequently’, on the other hand, when you want to imply that event two happened after event one; it followed sequentially in time, but no causality was necessarily involved.
- Lionel Messi scored for Barcelona, and subsequently scored again.
- Kanye West posts a woman’s nude picture, subsequently deletes it (if this D-list tittle-tattle interests you, here’s the link)