The difference is that the Heating and Cooling Loads Tool uses a Radiant Time Series Method (RTSM) calculation engine to calculate loads and the Systems Analysis load calculation tool uses a Heat Balance Method (HBM) calculation engine provided by EnergyPlus.
The RTSM typically calculates slightly more conservatively (the load calculated is higher than the true load imposed in real world conditions) while the HBM is typically more accurate, but may underestimate loads.
The RTSM calculates loads component by component, so you can see the load coming from the window, roof, internal, ect. The HBM only calculates one number for the load and you can't see which component is driving the load. EnergyPlus attempts to break that number back out into components, but does a poor job. For example, you may see a huge interzone load going between floors, even though that's impossible because both floors are at the same temperature setpoint. This isn't because the load is wrong, it's because the HBM doesn't lend itself to reporting.
The RTSM is what most engineers are used to looking at. It's what Trane Trace 700 uses.
As of now, it seems like the Heating and Cooling Loads tool will not be available in version 2022 onward, which is a shame because with Trane Trace 700 going offline there will not be a lot of RTSM engines available anymore.