Special honest verifier zero-knowledge and zero-knowledge property is defined as follows:
Special honest verifier zero-knowledge(SHVZK):There exists a polynomial-time simulator M, which on input x and a random t, outputs an accepting conversation of the form $(m_1,t,m_2)$, with the same probability distribution as conversations between the honest $(P,V)$ on input $x$
Zero-knowledge property(ZK): Let $(P,V)$ be an interactive proof system for some language L . We say that (P,V) is computational zero-knowledge if for every probabilistic polynomial-time interactive machine $V^*$, there exists a probabilistic polynomial-time algorithm $M^*$ such that the output of the interactive machine $V^*$ after it interacts with the interactive machine P on common input x is computationally indistinguishable from the output of machine $M^*$ on input x.
Assume, there exists a interactive-protocol $\pi$ for language $L$ which is three move protocol that satisfies zero-knowledge property
Considering $\pi$, the difference between SHVZK AND ZK is Simulator is constructed for only honest verifier in SVZK, whereas in ZK simulator must constructed for even cheating verifier.
Can we say $\pi$ satifies SHVZK?. My doubt is In SHVZK, simulator produces accepting transcript where as in ZK property there is no condition about acceptance of transcript generated by simulator.