The carbon market and the green bond market are important institutions for reducing greenhouse gas emissions and achieving economic low-carbon transformation. Accurately understanding the characteristics and correlations of the two markets is of great significance for promoting the achievement of the “dual carbon” goal. From the perspective of different time scales and market conditions, this study selected the maximal overlap discrete wavelet transform (MODWT) to decompose the price time series data of China’s carbon market and green bond market. The quantile Granger causality test was used to calculate the causal relationship between the two markets at different quantiles, and the association between the two markets was estimated based on quantile-to-quantile regression (QQR). The results show that, regardless of the time scale and market conditions, the Chinese carbon market is always the Granger cause of the green bond market. When the green bond market is in a slump state (i.e., in a “bear” market), it will have a certain negative impact on the carbon market in the short term, but in the medium and long term, the impact of the green bond market on the carbon market is positive. In addition, as the time scale increases, the synergistic effect between the green bond market and the carbon market becomes more and more significant. At medium- to long-term time scales, extreme market conditions can easily cause extreme shocks from the green bond market to the carbon market.