The intersection of blockchain and cloud technologies introduces transformative possibilities for reshaping business and organizational operations. Within this evolving landscape, the amalgamation of these technologies gives rise to novel deployment modes, referred to in this paper as Blockchain-Cloud Deployment Modes (BCDM). This paper provides an in-depth exploration and comparative analysis of these BCDM, emphasizing their capacity to enhance decentralization and scalability. The study investigates three distinct BCDM: Cloud over Blockchain (CoB), Blockchain over Cloud (BoC), and Mixed Blockchain Cloud (MBC). CoB leverages blockchain as a backend for storing and managing data within cloud applications, while BoC employs a cloud-based infrastructure for hosting and running blockchain applications. MBC, a hybrid approach, integrates CoB and BoC by deploying multiple blockchain instances on a cloud-based infrastructure. Critical parameters, including security, scalability, interoperability, and performance, serve as the basis for the comparative evaluation. Our findings unveil unique strengths within each BCDM. CoB excels in security and privacy, BoC demonstrates superior scalability and interoperability, and MBC emerges as a versatile architecture capable of addressing varied use cases. This research contributes valuable insights to the dynamic landscape of blockchain-cloud integration, empowering decision-makers to discern and adopt deployment modes tailored to their specific needs.