Artificial Intelligence (AI) has made remarkable advancements since its inception, with AI chips playing a pivotal role in this evolution. The advancement of specialized hardware, including Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs), has progressed rapidly in response to the increasing computational requirements of AI applications. Cloud-based AI leverages the vast computational resources of centralized data centers to handle large-scale data processing and complex model training, making it ideal for applications like large-scale data analytics, natural language processing, and scientific research. Conversely, Edge AI enabling real-time data processing and decision-making essential for applications with stringent latency, bandwidth, and privacy requirements, such as autonomous vehicles, health applications, and smart-city infrastructure. By examining the architectural advancements and real-world applications of both cloud-based AI and edge AI. This paper highlights the complementary strengths of these technologies and emphasizes the continued evolution and importance of AI hardware in driving innovation across various sectors, advocating for a balanced approach to enhance the full potential of both Cloud-based and Edge AI to create intelligent, responsive, and scalable solutions.