Cooking is a vital yet challenging activity for people with visual impairments (PVI). It involves tasks that can be dangerous or difficult without vision, such as handling a knife or adding a suitable amount of salt. A better understanding of these challenges can inform the design of technologies that mitigate safety hazards and improve the quality of the lives of PVI. Furthermore, there is a need to understand the effects of different visual abilities, including low vision and blindness, and the role of rehabilitation training where PVI learn cooking skills and assistive technologies. In this paper, we aim to comprehensively characterize PVI's challenges, strategies, and needs in the kitchen from the perspectives of both PVI and rehabilitation professionals. Through a contextual inquiry study, we observed 10 PVI, including six low vision and four blind participants, when they cooked dishes of their choices in their own kitchens. We then interviewed six rehabilitation professionals to explore their training strategies and technology recommendations. Our findings revealed the differences between low vision and blind people during cooking as well as the gaps between training and reality. We suggest improvements for rehabilitation training and distill design considerations for future assistive technology in the kitchen.