For IEEE 754-2019 basic formats, subnormal and denormal are synonyms. There are formats (like x87 80-bit as implemented in pre-387 hardware¹) that are not 754

For IEEE 754-2019 basic formats, subnormal and denormal are synonyms. There are formats (like x87 80-bit as implemented in pre-387 hardware¹) that are not 754 basic formats which admit non-normal encodings that are not subnormal (i.e. not smaller in magnitude than the smallest normal number). Some people used to call these "denormal" as well (even though the x87 docs call them "unnormal"), which caused confusion. "Subnormal" is unambiguous. In decimal IEEE 754 formats there are also non-canonical encodings, but these are neither subnormal nor denormal (decimal encodings are not, in general, normalized the same way binary floating-point is). ----- ¹ on 387 and later these are invalid encodings, and behave like a signaling NaN.