Rights issue is an offer made by the company to its existing shareholders to subscribe to additional equity shares at a discount. The primary reason for such issue is the infusion of capital (more money) which may be needed by the company for its operations or to pursue any M&A activity. It may also be used to increase the capital base of the company, which may arise in case of regulatory requirements. The shareholders who get the right can either subscribe to the shares at the discounted price, or may also trade the right in case they do not wish to subscribe to it.
Share split is splitting of face value of the share of the company into smaller value. This is generally undertaken to increase the liquidity of the share in the market as the number of shares increase (usually meaning that more retail shareholders can buy the share). Consequently, the shareholders now have additional shares in the company and the price of the shares are adjusted downward to adjust for the split.
Bonus issue is the process of giving an additional share to the existing shareholders of the company without any additional cost in the specified ratio. Therefore, the shareholders get additional shares in the company at zero cost. Much like share split, the market price of the shares adjusts to reflect the additional shares.
While both share split and bonus issues do change the value of the underlying company, many a times these announcements cause a temporary euphoria in the share price of the company.