Post History

The term (semantic) "shift" implies not just the emergence of a new meaning, but also abandonment of the old one.  The old meanings you refer to are still present in current English, so it is perhaps premature to speak of a semantic shift; this answer attempts to explain the emergence of the particular new meaning.

> I ask about Equity = Assets — Liabilities here, not its meaning as stock.

Incidentally, the former has developed from the latter, and both are just shorthand for the term "shareholders' equity".

That's about it, the rest is legal history of England more than linguistics.

Shareholders don't have an equitable[^1] interest in the net assets of a corporation while it lasts: the company owns those assets and liabilities, not the shareholders.  However, once the company ceases operation and is liquidated, shareholders become entitled to the proceeds[^2].  If all shareholders are of the same class, they can expect the proceeds to be distributed equitably[^3], i.e., fairly according to their number of shares.  This was historically an equitable chose in action[^4].  The proceeds equal the liquidated assets minus liabilities.

The term "equity", as a basic doctrinal principle, is invoked to protect symmetry between interests of (multiple) owners in a single company, even while the company is still incorporated.  It ended up called "equity" (in England) because "equity courts" and not "common law courts" would enforce former shareholder's access to what proceeded from the liquidation of a company.  Those equity courts connect to the 14th century usage which you traced which then referred only to that basic doctrinal principle[^5]; by that time, the institution which later became known as "equity courts" was still called "Chancery Division" or "chancery court".

This is roughly how the additional meanings which you encountered during your research fit together.


[^1]:Enforceable through courts of equity.  Or for that matter, though any other authority.

[^2]: If assets exceed liabilities.

[^3]: This word just suggests what "equity", as a principle of fairness, has to do with the liquidation proceeds of a company.  However, that is the modern understanding while the etymological path was different.

[^4]: Something owed to the ex-shareholder, enforceable through courts of equity.

[^5]: The principle comes from the Roman law term "aequitas naturalis", also called just "aequitas", or natural law (i.e., not a man made law), which stands in opposition to "ius aequum", a man made law based on natural law.  Likewise, the English word comes from Latin through Middle French.