The full-life data of machine is complex and abundant, requiring specialized and deep predictive models for accurate forecasts. However, achieving high prediction accuracy often increases model complexity, hindering edge deployment. To address this, several lightweight regression operators named single gated recurrent neural networks have been first proposed, striking a balance between accuracy and simplicity, and exploring the contribution of different gates in RUL prediction. In addition, during the whole degeneration process of machines, there exists global tendency and local vibration, different trends should be learned differentially. Thus, a novel lightweight differential learning mechanism called differential weighted information storage mechanism is proposed, which adopts different weight updated rules to make the weights store different trend information without any parameters added. Based on the above improvement, several lightweight single gated recurrent neural networks with the differential weighted information storage mechanism are first proposed. Then, deep learning frameworks are constructed by the proposed operators and adopted in gears and aero-engines RUL prediction. The experiment results show the outperformance of the proposed methods in accuracy and computation burden compared with recent works.