Random effect structure without correlation between intercept and slope My two models are roughly like this:
Y ~ A + (C+B||participant)+(1|B)

and
Y ~ A + ( C+ B || participant)

the difference being that for the first model, I have also specified a varying intercept by item 'B'.
Are both models the same?If not, what is the difference?
Do they include any correlation between the slope and the intercept?
 A: These models are not the same. The first model:
Y ~ A + (C+B||particiapnt)+(1|B)

does not make much sense because you are specifying that B is a grouping factor ( (1|B)) but then you are fitting random slopes for B, meaning that each level of B will vary with each level of participant. Apart from not making much sense, I would doubt that such a model would be identified.
The second model:
Y ~ A + ( C+ B || participant)

makes more sense, but note that by only including B and C as random slopes and not fixed effects, you are assuming that the overall slope of each is zero. This is also the case in the first model. It is more common, when specifying random slopes, to include the variable(s) as fixed effects too.
In both models, by using the || syntax you are forcing the correlation between the random slopes and the intercepts to be zero - no correlation will be estimated, whereas when you use the single | then the software will estimate the correlation between the random slopes and the random intercepts.
