A multifractal formalism is employed to analyse high-precision time-series data of Kepler stars with surface differential rotation (DR) traces. The multifractal detrended moving average (MFDMA) algorithm has been explored to characterize the multiscale behaviour of the observed time series from a sample of 662 stars selected with parameters close to those of the Sun (e.g. effective temperature, mass, effective gravity and rotation period). Among these stars, 141 have surface DR traces, whereas 521 have no detected DR signatures. In our sample, we also include the Sun in its active phase. Our results can be summarized in two points. First, our work suggests that star-spots for time series with and without DR have distinct dynamics. Secondly, the magnetic fields of active stars are apparently governed by two mechanisms with different levels of complexity for fluctuations. Throughout the course of the study, we identified an overall trend whereby the DR is distributed in two H regimes segregated by the degree of asymmetry A, where H-index denotes the global Hurst exponent that is used as a measure of long-term memory of time series. As a result, we show that the degree of asymmetry can be considered a segregation factor that distinguishes the DR behaviour when related to the effect of the rotational modulation on the time series. In summary, the multifractality signals in our sample are the result of magnetic activity control mechanisms leading to activity-related long-term persistent signatures.