Traditional recommendation models often rely on unique item identifiers (IDs) to distinguish between items, which can hinder their ability to effectively leverage item content information and generalize to long-tail or cold-start items. Recently, semantic tokenization has been proposed as a promising solution that aims to tokenize each item's semantic representation into a sequence of discrete tokens. In this way, it preserves the item's semantics within these tokens and ensures that semantically similar items are represented by similar tokens. These semantic tokens have become fundamental in training generative recommendation models. However, existing generative recommendation methods typically involve multiple sub-models for embedding, quantization, and recommendation, leading to an overly complex system. In this paper, we propose to streamline the semantic tokenization and generative recommendation process with a unified framework, dubbed STORE, which leverages a single large language model (LLM) for both tasks. Specifically, we formulate semantic tokenization as a text-to-token task and generative recommendation as a token-to-token task, supplemented by a token-to-text reconstruction task and a text-to-token auxiliary task. All these tasks are framed in a generative manner and trained using a single LLM backbone. Extensive experiments have been conducted to validate the effectiveness of our STORE framework across various recommendation tasks and datasets. We will release the source code and configurations for reproducible research.