Unsupervised Domain Adaptation (UDA) has shown promise in Scene Text Recognition (STR) by facilitating knowledge transfer from labeled synthetic text (source) to more challenging unlabeled real scene text (target). However, existing UDA-based STR methods fully rely on the pseudo-labels of target samples, which ignores the impact of domain gaps (inter-domain noise) and various natural environments (intra-domain noise), resulting in poor pseudo-label quality. In this paper, we propose a novel noisy-aware unsupervised domain adaptation framework tailored for STR, which aims to enhance model robustness against both inter- and intra-domain noise, thereby providing more precise pseudo-labels for target samples. Concretely, we propose a reweighting target pseudo-labels by estimating the entropy of refined probability distributions, which mitigates the impact of domain gaps on pseudo-labels. Additionally, a decoupled triple-P-N consistency matching module is proposed, which leverages data augmentation to increase data diversity, enhancing model robustness in diverse natural environments. Within this module, we design a low-confidence-based character negative learning, which is decoupled from high-confidence-based positive learning, thus improving sample utilization under scarce target samples. Furthermore, we extend our framework to the more challenging Source-Free UDA (SFUDA) setting, where only a pre-trained source model is available for adaptation, with no access to source data. Experimental results on benchmark datasets demonstrate the effectiveness of our framework. Under the SFUDA setting, our method exhibits faster convergence and superior performance with less training data than previous UDA-based STR methods. Our method surpasses representative STR methods, establishing new state-of-the-art results across multiple datasets.