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), philosophy, 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 to non-family members in the late 19th century—though perhaps only a portion of the full curriculum. 

Being a school of jujutsu, Daito Ryu consists of numerous throwing techniques, strikes, arm and leg locks, pins and immobilizations, and other control techniques. 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 emphasis on timing and blending, Daito Ryu can appear largely indistinguishable from Aikido. However, Daito Ryu can be considered a koryu (old school) where injuring and  maiming opponents is a matter of course in life-protection contexts, while in Aikido, this would go against its philosophy of peace, harmony, and love.

In short, the technical basis of Aikido is Daito Ryu Aikijujutsu. It is the philosophy, practice, and execution of techniques that separates the two arts.