Changepoint models are increasingly used to represent changes in the rate of warming in surface temperature records. On the opposite hand, a large body of literature has suggested long‐memory processes to characterize long‐term behavior in surface temperatures. While these two model representations provide different insights into the underlying mechanisms, they share similar spectrum properties that create “ambiguity” and challenge distinguishing between the two classes of models. This study aims to compare the two representations to explain temporal changes and variability in surface temperatures. To address this question, we extend a recently developed time‐varying spectral procedure and assess its accuracy through a synthetic series mimicking observed global monthly surface temperatures. We vary the length of the synthetic series to determine the number of observations needed to be able to accurately distinguish between changepoints and long‐memory models. We apply the approach to two gridded surface temperature data sets. Our findings unveil regions in the oceans where long‐memory is prevalent. These results imply that the presence of long‐memory in monthly sea surface temperatures may impact the significance of trends, and special attention should be given to the choice of model representing memory (short versus long) when assessing long‐term changes.