Many times soccer club and soccer academy are used interchangeably and can have the same or different meaning depending on who you ask. Generally, the most common difference between the two is that a soccer academy will have teams with specific age groups such as a U17, U15, U14, and so on, that compete with other teams.
On the other hand, a soccer club can also have specific age groups for teams but they might also have teams that compete against one another or compete with other club teams. A soccer club can also have different leagues within the organization and have players sign up to play in that league.
A soccer academy might not just let anyone signup, the players might have to be scouted and invited to join the academy. Either way, many people all over the world have different interpretations as there is no specific definition since may use them in different ways.