In term 1, you say P(z_k | x_k) is a probability (which should be a scalar value between 0.0 and 1.0 inclusive). How did we get from the vector pdfs of measurement and estimate to a scalar probability? Maybe you meant evaluating a pdf at an arbitrary point z_k, getting its density (scalar non-negative value, between 0.0 and infinity) at that point? I have the same confusion on your other enumerated terms. If they are probabilities, I'm only familiar with getting those by integrating the pdfs over some set of bounds or range.

I've seen the k subscripts plenty before, and some people use + and - to indicate pre and post parts of an operation, others put conditional vertical bars in the subscripts, but your definition for the pdf of z_k is a bit different than I'm used to. If we focus on the current instant of time (dropping the subscripts), ignore the motion model part, and only deal with a single measurement, I would say the estimate and measurement are defined like this:

    estimate    ~ Normal(mean=x, covar=P)
    measurement ~ Normal(mean=z, covar=R)

Then there is an elegant formula looking at it as an information filter, using Matlab-ish notation:

    Y = inv(P)    +  H'*inv(R)*H
    y = inv(P)*x  +  H'*inv(R)*z

    update ~ Normal(mean=inv(Y)*y, covar=inv(Y))

Ignoring the information filter stuff, and getting back to your list, Term 1 looks like a pdf with the dimensionality of z, but the result in Term 4 is a pdf with the dimensionality of x. In otherwords, the resultant Term 4 is a pdf (function) which takes a vector argument in the x space, and I don't see where to pick any given z for the pdf in Term 1.

It's getting late, and I'm getting spacey, but it's tempting to try and write the type signatures of these functions in some strongly typed pseudocode so I can show you my confusion.