Distributed attitude control for spacecraft formation without angular velocity measurement is complicated and challenging. Based on nonsingular terminal sliding mode, this paper designs two kinds of finite-time attitude synchronization controllers with inertia uncertainties and external disturbances. Aiming at calculating angular velocity in finite time, a nonlinear state observer and an angular velocity calculation algorithm are firstly developed. Then, two strategies for estimating reference signals and two distributed output feedback controllers, based on continuous adaptive technology and adaptive disturbance observer, are designed respectively. Different from existing results, the controllers are inherently continuous and the control chattering is greatly reduced. Also, the designed nonlinear observers need no prior knowledge on the upper bound of uncertain state and are proved finite-time convergent via Lyapunov theory. Finally, simulations and comparisons demonstrate the effectiveness of the proposed schemes.