Welcome to the forum.
".38 S&W Special" is the official name because Smith & Wesson created the cartridge over a hundred years ago. It's just shortened to ".38 Special" for brevity.
"CTG" is just an abbreviation for "cartridge".
It probably would be better to shoot standard pressure .38 Special ammo in that nice revolver instead of higher-pressure stuff marked "+P", though it would handle an occasional load of the hotter ammunition.
You'll enjoy shooting that gun, and it will still be going strong when your great-grandkids inherit it.