A bonus issue is where shares are issued 'free' to existing shareholders in proportion to their holding; e.g. in 1 for1 bonus issue, each shareholder is issued one new share at no cost for each 1 share held.
A share split is where the company splits each of the existing shares into a greater number of shares; e.g. in a 2 for 1 split, two "new" shares are issued by the company replacing each old share. The effect on market price of a 2 for 1 split should be exactly the same as a 1 for 1 bonus, but the process and accounting treatment is different.