Recent years have seen remarkable advances in the field of Simultaneous Machine Translation (SiMT) due to the introduction of innovative policies that dictate whether to READ or WRITE at each step of the translation process. However, a common assumption in many existing studies is that operations are carried out at the subword level, even though the standard unit for input and output in most practical scenarios is typically at the word level. This paper demonstrates that policies devised and validated at the subword level are surpassed by those operating at the word level, which process multiple subwords to form a complete word in a single step. Additionally, we suggest a method to boost SiMT models using language models (LMs), wherein the proposed word-level policy plays a vital role in addressing the subword disparity between LMs and SiMT models. Code is available at https://github.com/xl8-ai/WordSiMT.