What is the difference between shareholders' equity, equity, and book value?

Question

I have been doing some reading and I have found that shareholders' equity is equal to the company's total assets minus its total liabilities. Equity is apparently defined in much the same way. Book value is equal to the total assets minus intangible assets minus liabilities. So what is the actual difference between all of them?
Intangible assets seem rather hard to quantify, if I bought a house in a good neighborhood, its location could be called an intangible asset, right? But how do I measure this asset with a monetary value so that I can subtract it from its actual value?

Answer 1

Equity is defined as

The value of an asset less the value of all liabilities on that asset. [source]

This is a rather broad definition and equity can take on different forms. E.g., for a house, it is the difference between the market value of the house and the mortgage still owned by the owner.

In the context of a company balance sheet, we usually talk about Shareholder's equity, which, as Wikipedia puts it

represents the equity of a company as divided among individual shareholders of common or preferred stock

Contrary to the house example, the market value of a company, is the sum of all shares. And the shareholder's equity is that value (asset) subtracted from liabilities (creditors, etc.). See also this page.

The book value is the value of an asset. But the difference with the Shareholder's equity is illustrated as

To find a company's book value, you need to take the shareholders' equity and exclude all intangible items. This leaves you with the theoretical value of all of the company's tangible assets which are those assets that can be touched, seen, and felt as opposed to things such as patents, trademarks, copyrights, and customer relationships. [source]

Answer 2

Book value of an asset is the carrying value of an asset in the books i.e. balance sheet of the company. I think you are confusing the definitions of net asset value and book value.

Equity and shareholders' equity are referring to the same thing. Shares are recorded in balance sheet at book value, any additional payments are recorded as paid in capital to account for the difference between market and book value.

So you have a book value for shares and a market value.