Open-set Recognition (OSR) aims to identify test samples whose classes are not seen during the training process. Recently, Unified Open-set Recognition (UOSR) has been proposed to reject not only unknown samples but also known but wrongly classified samples, which tends to be more practical in real-world applications. In this paper, we deeply analyze the UOSR task under different training and evaluation settings to shed light on this promising research direction. For this purpose, we first evaluate the UOSR performance of several OSR methods and show a significant finding that the uncertainty distribution of almost all these methods is actually closer to the expectation of UOSR than OSR. We show that the reason lies in the known but wrongly classified samples, as their uncertainty distribution is extremely close to unknown samples rather than known and correctly classified samples. Second, we analyze how the two training settings of OSR (i.e., pre-training and outlier exposure) influence the UOSR. We find although they are both beneficial for distinguishing known and correctly classified samples from unknown samples, pre-training is also helpful for identifying known but wrongly classified samples while outlier exposure is not. In addition to different training settings, we also formulate a new evaluation setting for UOSR which is called few-shot UOSR, where only one or five samples per unknown class are available during evaluation to help identify unknown samples. We propose FS-KNNS for the few-shot UOSR to achieve state-of-the-art performance under all settings.