Order ID refers to an integer, while "order" refers to string.
If you want to use ID (Edit menu -> Display values as Raw object Data), the function becomes IssueTargetOrderById(), where in the place of the order an integer is set, e.g. 852676, unlike IssueTargetOrder(), where you place a string, e.g. "attack".
If you want to check how each unit event response is translated in Jass, create a trigger with the action "Unit - Kill unit". Pick the unit type you want (E.g. Damage source) and convert the trigger to Custom script). There, you have the Jass counterpart.