A smart phone was a type of mobile phone.
The Twelfth Doctor noted they were a product of parallel evolution, and would always get started wherever there were people. (TV: The Doctor Falls)
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 dictation for a book he was writing 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)
Adam Mitchell had a smart phone in 2012. (AUDIO: The Other Side)
From 2013 on, Clara Oswald had an iPhone. (TV: The Time of the Doctor, etc.) 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)
The Coal Hill students who comprised the Coal Hill Year 8 Gifted and Talented Group all had iPhones. They used Samson's to take selfies. (TV: In the Forest of the Night)
Courtney Woods, on a TARDIS trip, used her iPhone to post pictures of the Twelfth Doctor on the Moon onto Tumblr in the year 2049. (TV: Kill the Moon)
In 2020, Tania Bell gave smart phones to the Eighth Doctor, Liv Chenka and Helen Sinclair, although Liv declined to keep it. (AUDIO: Wild Animals)
Alice Wu got a smartphone for Christmas which was promptly possessed by The Wire and decimated by The Tenth Doctor and his sonic screwdriver. (PROSE: Loose Wire)
Giles used a smart phone whilst staring at Lucifer from across a street. (WC: Mission: Find Lilith [+]Loading...["Mission: Find Lilith (webcast)"])