The Minus tool has been there since a long time (even in ArcMap). It is available with extensions like 3D Analyst or Spatial Analyst (ArcMap/ArcGIS Pro) or Image Analyst (only ArcGIS Pro). It will give you an absolute difference between the pixel values of the two raster datasets.
Compute Change Raster is a newly added tool available with Image Analyst for ArcGIS Pro (ver. 2.7 and later). This tool can calculate not only the absolute difference (like Minus tool), but also relative difference and categorical difference between the two raster datasets.
Check the links for more details.
In a sense, yes. You get the positive and negative values.
But It doesn't actually classify the data. But you can classify the output Raster's symbology as <0 and >0 (or whatever number of classes you desire).
If you want to change the actual output Raster values to binary (a number of classes), use Reclassify tool.
No... not in general, minus returns the numeric difference between data sets. The difference need not be positive or negative and it need not be binary!