difference between single index and multiple index

[H H]

Is there an advantage or disadvantage to creating multiple individual indexes on columns vs. a single index with multiple columns? IOW:

ALTER TABLE `cc_auth_dtl`
ADD INDEX `site_id` (`site_id`);

ALTER TABLE `cc_auth_dtl`
ADD INDEX `business_date` (`business_date`);

VS.

ALTER TABLE `cc_auth_dtl`
ADD INDEX `site_id_business_date` (`site_id`, `business_date`);

Is one faster or slower than the other? Are there any other differences? Thanks!