A smart phone was a type of mobile phone.
Rory Williams had one in 2008. It was also a camera phone. He used it to take photos of patients which he had seen around the village of Leadworth, who were supposed to be in a coma. (TV: The Eleventh Hour) After he and his wife Amy Pond settled into their new lives stranded in the early 20th century, (TV: The Angels Take Manhattan) in 1946 Rory used a smartphone to record a video message for his incoming adopted son Anthony Williams, during which he cited it as being the "only working smartphone in the world". (WC: Rory's Story)
From 2013 on, Clara Oswald had an iPhone. (TV: The Time of the Doctor, et al.) While in Clara's form, Bonnie used the phone to record video and send and receive video calls, while Clara, connected to Bonnie's mind, sent text messages to the Twelfth Doctor without Bonnie realising. The Twelfth Doctor also has an iPhone at this time. (TV: The Zygon Inversion)