Is equity, book value and carrying value essential the same thing?

Can these terms be used interchangably?

I know that equity and shares/stock can be used interchangably.

According to CFAI

equity = Assets less liabilities; the residual interest in the assets after subtracting the liabilities.

book value = The net amount shown for an asset or liability on the balance sheet; book value may also refer to the company’s excess of total assets over total liabilities.

To me, they both indicating the same thing, ie total asset minus total liability.

Also what is the difference between these two and book value of equity?

Thanks for the clarification.

Equity = Book value of equity = book value. All reflecting th value of equity on the balance sheet. Though the term “equity” is kind of broad and random and would usually depend more on the context.

As far as carrying value which is in your title but not mentioned in the post: The carrying value depends on the type of asset & type of classification. PP&E could be held at historic cost less depreciation, it could be revalued and held at that value as well. Investments could be held for trading, held to maturity etc.