First to IFSQN Vu!
Secondly those terms are rarely used in my experience however I have heard the various GFSI systems (like SQF, BRC, IFS, FSSC) called schemes before however I haven't seen them called that directly in documentation.
HACCP, I believe, is considered a system. HACCP is the systematic collection and mitigation of food safety hazards through a certain set of steps used in order. Also the entirety of your food safety is called the food safety management system because it encompases all of your programs, controls, documentation, training, etc. that is being used to keep your food safe for the food chain.
Tools are things that help us accomplish our goals. Things like fishbone diagrams and other root cause analysis tools help us to find the actual reason for a deviation so we can implement controls to make sure they don't happen again.
I'm not sure those terms are really the ones you need to get wrapped up in. "System", "Scheme", "Program", "Tool", etc. In FSSC it is much more important to understand PRP, oPRP, CCP, etc. Those are the things that are put in place (or going to be put in place) to mitigate the hazards with your food to make sure it's safe for your customers.
I'm sure if some people have more experience with these exact terms they'll throw more information in. But in my experience those are not the terms that someone needs to focus on.