Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods are cornerstone techniques for Bayesian inference and stochastic optimization. The multiple-try Metropolis (MTM) algorithm generalizes the Metropolis-Hastings (MH) scheme by selecting the next state from a set of weighted candidates, improving exploration of the state space. Particle Metropolis-Hastings (PMH) integrates MCMC and SMC ideas to efficiently tackle high-dimensional targets with sequentially factorized structures, embedding a particle filter within an MH framework. While both approaches have been extensively studied, particularly for state-space models, their relationship has not been fully explored. In this work, we examine the connections and distinctions between MTM and PMH schemes, which motivates the design of novel, highly efficient algorithms for filtering and smoothing. Among these, we introduce a particle multiple-try Metropolis (P-MTM) method, which demonstrates excellent performance across a range of numerical experiments.