In this paper, a two-user collaborative secret and covert uplink transmission scheme is proposed for unmanned aerial vehicle (UAV) secure communication. Specifically, two ground legitimate users, named Bob and Carlo, transmit their signals to the UAV using the non-orthogonal multiple access (NOMA). The content security requirement user employs the channel inversion power control (CIPC) method to transmit the secret signal, thereby complicating the adversary's detection of the covert signal. Considering the uncertainties of the adversary's position and noise, we derive a closed-form expression of the minimum detection error probability (DEP). To characterize the CIPC-aide joint secret and covert communications in the UAV NOMA system, we establish an optimization problem to maximize the sum of secret and covert rates subject to the constraints of DEP and the transmit power. Furthermore, we derive a closed-form solution to the problem and reveal the influence of key parameters on the sum rates, analytically and numerically. Our results provide new insights for multi-user secure uplink communication in UAV systems.