A smart building uses connected systems and sensors so that heating, lighting, ventilation, access and security respond to what is actually happening rather than to a timer. The building management system is the traditional control layer; sensors and occupancy data are what let it react rather than simply run.
A smart office is the workplace experience inside that building. The two meet at occupancy: if the building knows which floors are booked and occupied today, it can condition the space in use and leave the rest alone. That is usually where the energy saving comes from, and it needs booking data, not just sensors.