One site suggested the difference is that the warrant in the bond with warrant is a fixed price on company stock. E.g. for a \$1000 bond, you can buy 500 shares at \$2 each. And that convertible bonds does not have a fixed price term.
Another site suggested that with a bond with warrant, the warrant can be sold separately from the bond, while a convertible bond has not that possibility.
Are any of these suggestions correct, or is it something else that make up the (major) difference?