Even if useful definitions for the terms "metal" and "semi-metal" are 300 years old, as I have said, many modern manuals either do not give any proper definition for the term "metal", or even if they do they do not follow it consistently, so sometimes they apply the word "metal" to substances like bismuth, whose only resemblance to a metal is having free electrons. If this rule were followed consistently, graphite would also have to be named "metal", but no manual does that.
While having free electrons may be the most important property of metals for electrical and electronics engineering, for mechanical engineering and for manufacturing any kind of devices, the other property of metals, ductility, is far more important. This is why the distinction between ductile metals and intrinsically fragile semi-metals is very important.
In this case, the use of the word "metal" for bismuth is a clear cause of confusion, as it suggests an aromatic ring made of electro-positive atoms, which would be a real surprise. An aromatic ring made of atoms with the electro-negativity of bismuth is no surprise.
The elements with high electro-negativity, which in elemental form are semi-metals, semiconductors or non-metals, form covalent bonds between their atoms.
The elements with low electro-negativity, which in elemental form are true metals, form metallic bonds between their atoms.
So the expected chemical behavior for "metals" and for "semi-metals" is quite different.