A technical product manager at Amazon is generally referred to as a Product-Manager-Technical (PM-T). A PMT can have ownership over a product, a functional area or even a program, but their primary focus is on formulating the vision, the strategy and roadmap for that area. They are also ultimately responsible for the end metrics of adoption, quality and effectiveness of the features they deliver. They are also the primary customer champions synthesizing their current pain-points, as well as anticipating future needs. They develop concept documents (PRFAQs), Business Requirements, and Product Definitions. These are not exclusive to PMTs since Amazonian culture drives the notion of ownership, customer obsession and invention into everyone, but these are responsibilities that are more core to PM/PMTs.
A Product Manager (PM) shares all of these same qualities and responsibilities with a lower bar on technical expertise which may be more suited for specific roles involving less-technical products or less-technical functional areas within a larger portfolio.
A Technical Program Manager (TPM) is a distinct role that sits at the intersection of product, engineering and program management. An Amazon TPM is a unique role that combines business ownership over delivery with high-level technical architecture. They are usually the program glue - that brings together PMTs, engineering teams and business stakeholders on all aspects of an initiative. To address a common misperception, TPMs are not project managers, but have far more involvement in business outcome, product decisions and typically posess engineering and architcture skills that allow them to coordinate efforts across product areas.
However, note that this AMA is focused on the technical product-manager role or PM-T. So please make that translation whenever you see "TPM" in these questions.