I think the confusion comes from the fact that many people interchange words, so it depends on who you are talking to.
Others may correct me, but my understanding is that the music and dance are interwoven so a piece may be called "Diansa", but a number of musicians and dancers work together to perform the piece.
Sometimes people refer to what the musicians play as the song or rhythm.
My djembe teacher refers to parts. So he will speak of the part for one djembe player in a piece.
Within each players part there are a number sections what my teacher calls phrases. These phrases might correspond to a section of music on any instrument or section such as an introduction, a call (indicates some sort of change), a solo, a phrase repeated for a long time, a phrase to speed up a passage etc., so that a number of phrases make up a part.
Sometimes people break down a phrase into a number of repeated units that are referred to as patterns or rhythms. An example would be the tab at the bottom of the video lessons page - sometimes people call this the "pattern" or "rhythm" for Diansa.
I think it is better to think in terms of parts and phrases instead of rhythms and patterns. To teach, and instructor has to say "this phrase sounds like this" - if you watch my hands they do this (while showing a "pattern of movement of the hands" Otherwise, what tends to happen is people learn a particular "string of drum tones" they think is rhythm and say "Oh, THIS is Diansa".
Learning from books is great and always there when you feel like playing. However, one doesn't really get the sense of what a song feels like without the rest of the musicians in a full African orchestra. So, if you get a chance, see if you can find a good teacher or at least some others so you can hear all the parts of the songs you learn, if you haven't done this already.
Hope this helps and good luck with the playing.
I'm sure there are a lot of opinions on this so I'd like to hear what others say.