In this paper we study yrast states of Sn-128,Sn-126,Sn-124 and Sn-104,Sn-106,Sn-108 by using the monopole-optimized realistic interactions in terms of both the shell model (SM) and the nucleon-pair approximation (NPA). For yrast states of Sn-128,Sn-126 and Sn-104,Sn-106, we calculate the overlaps between the wave functions obtained in the full SM space and those obtained in the truncated NPA space, and find that most of these overlaps are very close to 1. Very interestingly, for most of these states with positive parity and even spin or with negative parity and odd spin, the SM wave function is found to be well represented by one nucleon-pair basis state, viz., a simple picture of "nucleon-pair states" (nucleon-pair configuration without mixings) emerges. In Sn-128,Sn-126, the positive-parity (or negative-parity) yrast states with spin J > 10 (or J > 7) are found to be well described by breaking one or two S pairs in the 10(1)(+) (or 7(1)(-)) state, i.e., the yrast state of seniority-two, spin-maximum, and positive-parity (or negative-parity), into non-S pair(s). Similar regularity is also pointed out for Sn-104,Sn-106. The evolution of E2 transition rates between low-lying states in Sn-128,Sn-126,Sn-124 is discussed in terms of the seniority scheme.