With the rapid development of mobile Internet technology, on-demand car-hailing services have become essential for people's daily commuting. Order dispatch is a critical problem in on-demand car-hailing services. However, in most existing works, the service provider is asked to set a unified pick-up distance to prevent long waiting time for requesters. Indeed, different requesters have different tolerance for pick-up distance, and some requesters may accept longer pick-ups if offered discounts for payment. Regarding this fact, we formulate discount-based order dispatch as a coupling of two subproblems, discount determination and order dispatch, aiming to dispatch more orders and thereby more platform profits. We propose customized methods to solve the problems for shared and non-shared mobility services, respectively. We also conduct extensive experiments to evaluate the effectiveness and efficiency of our proposed methods on a real dataset, which shows that our methods can achieve 170% improvements in non-shard services and 43% improvements in ridesharing services on average in terms of attained profit compared to the widely adopted baselines.