Does the Law of One Price hold for Stocks AND Bonds?

If you mean identical goods sell at identical prices, then yes. A bond of the same issuance will always sell for the same price as any other bond of the same issuance (as well as a stock).

I you mean 2 stocks of similar companies, well no. The aren't identical enough.

or a stock and a bond, are they considered "substitutes"?

uh, no, not at all

Not at all

Stocks and bonds are inherently different. Stocks are part ownership in a company, entitling you to its profits. Bonds are loans to a company, entitling you to a repayment of the loan as well as a predetermined interest payment.

In other words, i'm going to charge different amounts to a) lend Bear Stearns money, or b) buy a piece of Bear Stearns, expecting to receive part of its profit from its continued operations.

In the context of primary markets, stocks and bonds essentially provide an entity with identical financing (think "uses" of capital); however, with bonds your expected return is explicit, while equity returns are implicit (and subordinate).

I assume you differentiate stocks and bonds as they are different asset classes.

If there are structural breaks, trade barriers, etc. or if investors behave irrationally or exhibit biases, e.g. home bias, there is no reason why the law of one price should hold.

Neither the market for stocks or bonds is perfectly efficient so the Law of One Price doesn't apply to either apart from in a textbook.

Each market has a certain amount of "One-ness" but in different ways; for equities you have the structural transparency of the market in its favour, for bonds you have the underlying maths.

Now back to work for me - have a bunch of subprime guys I need to fire.