Both are departure choices for Kyoto on the Tokaido Shinkansen. In the reservation form, Tokyo means Tokyo Station, not whichever station is nearest your accommodation. Shinjuku and Shibuya require a local connection before this Shinkansen journey.
Compare your hotel's door-to-station route, stairs and number of transfers. Tokyo Station may fit a stay near Marunouchi or the station itself; Shinagawa can be a useful alternative when your local connection reaches it more easily. There is no single best departure station for every Tokyo hotel. Book your actual boarding station rather than assuming two bookings are interchangeable.
Use JR Central's station maps for Tokyo, Shinagawa and Kyoto. At Tokyo Station, follow Tokaido/Sanyo Shinkansen signs, not just any sign saying Shinkansen. Match the departure board's train number and time to your booking; the platform is not determined by your destination alone.
Our planning allowance is to reach the departure station 30–45 minutes before the train, longer if you need ticket help, lifts or food. This is an editorial buffer, not a railway check-in deadline. Buy a lunch box before boarding if that avoids arriving hungry in Kyoto.