In recent years, the rapid evolution of satellite communications play a pivotal role in addressing the ever-increasing demand for global connectivity, among which the Low Earth Orbit (LEO) satellites attract a great amount of attention due to their low latency and high data throughput capabilities. Based on this, we explore spatial modulation (SM) and space shift keying (SSK) designs as pivotal techniques to enhance spectral efficiency (SE) and bit-error rate (BER) performance in the LEO satellite-assisted multiple-input multiple-output (MIMO) systems. The various performance analysis of these designs are presented in this paper, revealing insightful findings and conclusions through analytical methods and Monte Carlo simulations with perfect and imperfect channel state information (CSI) estimation. The results provide a comprehensive analysis of the merits and trade-offs associated with the investigated schemes, particularly in terms of BER, computational complexity, and SE. This analysis underscores the potential of both schemes as viable candidates for future 6G LEO satellite-assisted wireless communication systems.