What convertible securities are
Convertible securities are typically either bonds or preferred stock that combines typical features of their respective asset class with exposure to price changes in the common shares of the company. Convertible bonds will usually carry an interest rate, par value, and maturity date just like any other bond. Convertible preferred stock will have a stated preference amount in the event of liquidation, and it also often has a set dividend rate that acts much like a coupon rate for a bond.
Convertible securities also give investors the right to exchange their bond or shares for common stock of the company. Each convertible security will give specifics on the number of shares you'll receive upon conversion, as well as the expiration date by which the security must be converted. In some cases, conversion is mandatory, while other convertible securities leave the conversion decision at the discretion of the owner.
What warrants are
Warrants, on the other hand, typically don't have any intrinsic value of their own. Unlike convertible securities, there's no underlying bond or preferred shares that give the warrant owner any additional rights. The only value that the warrant has comes from its conversion feature.
Warrants resemble options in that they typically require investors to make an additional payment within a specified time frame in order to exercise the warrant and receive common stock in exchange. Warrants tend to have longer lifespans than ordinary options, with expiration dates as much as 10 years into the future being relatively common. Investors aren't required to exercise warrants, but they're worthless after they expire unexercised.
Both warrants and convertible securities have their place within the capital structure of a company. The investments have some things in common, but their differences also have maximum value to different sets of investors. Those who want maximum reward will prefer warrants, but those who want some protection from worst-case scenarios will gravitate toward convertible securities.