For a conditionally independent joint distribution, there are some variables which are dependent on each other and on the other hand, there are some variables which are independent. You can say it a partial dependency/indepedency.

^[1]As an example, if there are 3 random variables $(x_1,x_2,x_3)$ and $x_1$, $x_2$ are independent and $x_3$ depends on $x_1$ then the joint probability equation will be,

if they can take, 2, 3, 4 variables respectively, then,

For $p(x_1)$, there are 2 parameters,
for $p(x_2)$, there are 3 parameters,
and for $p(x_3|x_1)$ there are 2 * 4 parameters

In total there will be 2 + 3 + 2 * 4 = 13 parameters.

Between Fully Joint Distribution (all dependent) and Fully Independent Joint Distribution (all independent); factorizes using Conditional Probability.

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