Entanglement detection and classification of different kinds of entangled states in quantum many-body systems have always been a key topic in quantum information and quantum computation. In this work, we investigate the entanglement detection and classification of three special entangled states: $4$-qubit GHZ state, $4$-qubit $W\overline{W}$ state, and $4$-qubit SGT state, which cannot be distinguished by the general quantum Fisher information (QFI) under the usual local operations. By utilizing the experimentally mature and controllable one-axis twisting model, accompanied by the optimized rotation and adjustable interaction strength, we successfully classify the three states by QFI. Besides, we have also studied the effects of four types of environmental noises on the entanglement detection, \textit{i.e.}, bit-flip channel, amplitude-damping channel, phase-damping channel, and depolarizing channel. The results show that under the local operation, the change of the QFI from the $4$-qubit GHZ state with respect to the decoherence parameter $p$ in four noise channels is significantly different from those from the $W\overline{W}$ state and SGT state, and it can be distinguished. However, the QFI from the $W\overline{W}$ state and the SGT state exhibit the same variations and cannot be classified. In the one-axis twisting model, the variation curves of the QFI from the three states under the four noise channels are mutually distinct and can be clearly observed. It should be noted that, in the bit-flip channel, the QFI of the $W\overline{W}$ state and the SGT state overlaps in the middle region ($p\approx0.5$), failing to be classified. Our work provides a new way to realize the entanglement detection and classification in quantum many-body systems, which will contribute to the future research in quantum science and technology.