The terminology has gotten messy over the years, as with many Busse models, as variants and show specials have come along that don't fall into the formerly neat categories.
The CGFBM was first. Sold from the Busse site, in different finishes and scale options. The blade was 0.25" thick, with a very high sabre grind; ie, there was only a narrow flat area above the primary grind. The primary grind itself was something of a convex, with a very slight curvature if you put a straight edge on it.
The Heavy Heart FSH came later, as a special offering from the Busse Company Store. All were made in black coating, with black micarta scales. 200 made/sold in standard thickness scales, another 200 in magnum scales. The blade was 0.27" thick, in a sabre grind as pictured above. As time went by, these became highly desirable on the resale market. IMHO, the term 'HHFSH' should be reserved only for this run of 400.
As the Busse production capacity was increased, the shop started making FSH again for shows and 'Ganzas. Some thick, some thin. A goodly number have been made in satin finish, at 0.27" thick, with a sabre grind, in various G10 scales. Many folk are calling these HHFSH. They are absolutely great knives, but not the real deal HHFSH.
As always, buyers need to educate themselves, ask questions, and not make any assumptions about what a knife is based on the name in the sales ad.