Is The Family (RE6) also The Connections (RE7&9)?

Both are said to be responsible of the cover-up of the stuff that happened in Raccoon City (in their respective games) and i think it would make the most canonical sense. The Family couldve been renamed to The Connections after the events of RE6 due to Simmons being dead. I think the best way that this could be confirmed is if the logo for The Connections is similar to the logo for The Family (im talking about their ring thingy) Any thoughts?