Aikido and Aikijujtsu
At Calgary Rakushinkan we practice Ishikawa Sensei's art of Aikido called "Ki to Tanden no Aikido"
We also practice Yamamoto ha Daito Ryu Aikijujutsu of the Shinto Jyushin Kai.
Aikido is the art developed by Morihei Ueshiba which was a synthesis of his martial arts (mainly Daito Ryu), philosphy and religion. His practice and teachings evolved over his life resulting in the inheritors disseminating various instantiations of the art depending on when and where they were taught, and of course their own experience, interpretations and interests. This is why there are many Aikido organizations, each with their own flavour.
Daito Ryu Aikijujutsu (or Daito Ryu Jujutsu or simply Daito Ryu) is the martial art of Takeda Sokaku. He is considered the founder of Daito Ryu, but is better thought of as the restorer or revealer of the art as it is the Takeda family martial arts that Takeda Sokaku began teaching not non-family members in the late 19th century (or a portion thereof).
Being a school of jujutsu, Daito Ryu consists of numerous throwing techniques, strikes, arm and leg locks, pins and immobilizations and so on. Some of the distinguishing characteristics of this school would be the context; for example, formal situations where arms are restricted or limited or other situations where arms are available. Also, Daito Ryu emphasizes timing and blending to neutralize attackers techniques and use their power against them. In this it is largely indistinguishable from Aikido. However, Daito Ryu can be considered a koryu (old school) where injuring, maiming or killing enemies is a matter of course while in Aikido, this would go against its philosophy or peace, harmony and love.
In short the technical basis of Aikido is Daito Ryu Aikijujutsu. It is the philosphy, practice and execution of techniques that separates the two arts.