What is the difference between nucleotide polymorphism (θ) and nucleotide diversity (π)?
You are also confusing definition of these terms with their expected values (typically computed from coalescent theory). Let's look at an example.

Consider a haploid population of 6 individuals. We will represent these individuals with 5 sites that can take values 0 or 1.

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Polymorphism

In this population there are $S=2$ polymorphic sites. In other words, there are two sites for which different individuals take different values in the population. Over these 5 sites, the fraction of polymorphic sites is $\frac{2}{5}$. You use $\theta$ for this quantity but to me, $\theta$ is typically used as a short hand for $2 N \mu$ (or $4 N \mu$ for diploid populations).

Under an infinite allele model, in a single panmictic haploid population (without selection and other assumptions), $E[S] = 2 N \mu a$, where $a = \sum_{i=1}^{k-1} \frac{1}{i}$, where $k$ is the sample size.

Genetic diversity

Genetic diversity is also known as expected heterozygosity. While it is most often called $\pi$, I will call it $H$ to avoid confusion. Imagine, you randomly sample two individuals in the population, what is the probability that there have different alleles at a given locus? 


At locus 1, $H = 0$
At locus 2, $H = 0$
At locus 3, $H = 0$
At locus 4, $H = 2 \frac{2}{5} \frac{3}{5} = \frac{12}{25}$
At locus 5, $H = 2 \frac{1}{5} \frac{4}{5} = \frac{8}{25}$


You can average over all loci if you want.

The expected heterozygosity in panmictic population (without selection and other assumptions), $E[H] = \frac{4 N \mu}{1 + 4 N \mu}$. You should notice a relationship between $H$ and $F_{ST}$ here!

Nucleotide diversity

The nucleotide diversity is the equivalent of $D$ from Nei and Li (1979) and is highly related to $D_{XY}$ (Nei, 1987). Once you've managed to demonstrate that the expected coalesence time is $N$ (I won't do the demonstration here), then under an infinite site model, the number of mismatch between two individuals is logically $E[D] = 2 N \mu$ (it is the number of mutations that has happened in both lineages since the the coalescence event). For diploid population, multiply everything by 2.

Relatedness between $D$ and $S$

Under a neutral model $\frac{S}{a} = D$. Actually the standardize difference between $\frac{S}{a}$ and $D$ is what is used in Tajima's $D$ tests.

Source of information

Hartl and Clarck is good IMO but I would also like to recommend reading Population Genetics: A Concise Guide by Gillespie who explain all of that wonderfully.