Human label variation arises when annotators assign different labels to the same item for valid reasons, while annotation errors occur when labels are assigned for invalid reasons. These two issues are prevalent in NLP benchmarks, yet existing research has studied them in isolation. To the best of our knowledge, there exists no prior work that focuses on teasing apart error from signal, especially in cases where signal is beyond black-and-white. To fill this gap, we introduce a systematic methodology and a new dataset, VariErr (variation versus error), focusing on the NLI task in English. We propose a 2-round annotation scheme with annotators explaining each label and subsequently judging the validity of label-explanation pairs. \name{} contains 7,574 validity judgments on 1,933 explanations for 500 re-annotated NLI items. We assess the effectiveness of various automatic error detection (AED) methods and GPTs in uncovering errors versus human label variation. We find that state-of-the-art AED methods significantly underperform compared to GPTs and humans. While GPT-4 is the best system, it still falls short of human performance. Our methodology is applicable beyond NLI, offering fertile ground for future research on error versus plausible variation, which in turn can yield better and more trustworthy NLP systems.