When bonds are issued and traded, their are strong implications to any relevant laws and regulations that apply. National bond markets include all the bonds that are issued and traded in a specific country, and denominated in the currency of that country; bonds issued by entities incorporated in that country are domestic bonds, where if they are incorporated in another country they are foreign bonds.
Bonds issued and traded on the Eurobond market are Eurobonds (named after their currency denomination). Eurobonds are typically less regulated than domestic as they are issued outside the jurisdiction of any single country. Most Eurobonds are bear bonds (trustees do not keep records of who owns the bonds; only the clearing system knows who the bond owners are).
Domestic and foreign bonds are registered bonds (ownership is recorded by either name or serial number). Global bonds are issued simultaneously in the Eurobond market and in at least one domestic market. Note that the denomination of a currency has a stronger effect on its price than where the bond is issued or traded, as it has a strong influence on the market interest rates.
Another implication to consider is the legal identity of the bond issuer and its legal form. For instance, obligations to make the contractual payments is assigned to the bond issuer. For securitized bonds, obligation to repay the bondholders often lies with separate legal entities (SPEs or SPVs).