Is the US bond market similar to a company's bond or share market?

Similar in that it sells bonds or shares to raise money, and it is in essence being "loaned" that money by the purchaser of its stocks or bonds and when it is demanded repayment by the shareholder or bond holder (after the bonds term of course) than it MUST pay that money back. In essence is the US bond market very similar to this?
All of the trillions it owes is mostly bonds , and is basically an account of money that is raised to fund its expansion. people trust that that expansion will occur and they will get their money back with interest.
And people trust that the US military will gurantee a good safe economic future.

Sort of a long winded question.

There is a slight difference. China and Japan and the oil exporters are the main purchasers of U S bonds. They buy them because the alternative is too frightening for them to contemplate. That is a collapse in the value of the dollar. Whereas companies for the most part are able to earn revenue to pay back their debts and most companies tend to keep their debts within limits. That does not apply to the U S.

The U S is essentually bankrupt, but if the purchasers of the U S debt acknowlege that they have a problem. All the trillions they hold in U S debt becomes worthless, so they keep buying to support the value.

Yes correct

Government Bonds are a way for the government to borrow money from the public just the same way a company might. Government bonds are considered very safe, hence the motto of the London stock exchange - "My word is my bond".

I wouldn't entirely agree that everyone thinks the military is the principal guarantor of a safe economic future.