Options are issued through the options exchange. Warrants are issued directly by companies and financial institutions.
Warrants are custom contracts and are less easy to trade than shares and less easy than standard options contracts.
The issuer of the warrant determines the contract size, the exercise price and the term. With options, the contract size is the same for all options. For share options, for example, the standard is 100 shares.
With a warrant, there is only one exercise price and one term. With options, there are different option series for each underlying asset with different exercise prices and terms. The options exchange regularly releases new options series, as long as the underlying asset meets certain conditions.
Warrants can only be bought, not written. Options can be bought and written.
The term of a warrant is generally somewhat longer than that of options, usually the term is several years.