Meiosis can produce genetically different haploid products even when every chromosome segregates correctly. Two major sources are independent assortment of homologous chromosome pairs and meiotic crossover.

Each homolog pair can orient in either direction

At metaphase I, the two homologs of a chromosome pair are attached toward opposite spindle poles. Which homolog faces which pole is not predetermined by the chromosome's parental origin.

For one homolog pair there are two possible orientations. Label its two copies $A_1$ and $A_2$:

orientation 1:  A1 → pole 1, A2 → pole 2
orientation 2:  A2 → pole 1, A1 → pole 2

A second chromosome pair, with homologs $B_1$ and $B_2$, can orient independently of the first. With two chromosome pairs, the whole-homolog combinations can therefore be

A1 B1     A1 B2     A2 B1     A2 B2

before considering crossover.

This is independent assortment: the metaphase-I orientation of one chromosome pair is, to a first approximation, independent of the orientation of a different chromosome pair.

For $n$ independently assorting chromosome pairs, there are $2^n$ possible combinations of whole parental-origin homologs before crossover is considered.

Crossover creates recombinant chromatids within a chromosome

Independent assortment reshuffles whole homologs. Crossover reshuffles DNA within homologous chromosome pairs.

If nonsister chromatids exchange corresponding segments during meiotic recombination, a resulting chromatid can carry one chromosome region derived from one homolog and another region derived from the other.

Thus a haploid meiotic product need not contain an intact version of either original homolog. It can contain a recombinant chromosome.

The two mechanisms operate at different scales

independent assortment → which homolog enters which product
crossover              → which DNA segments are combined within a homolog

Together they generate many possible chromosome combinations before any new sequence changes are considered.

Random does not mean unconstrained

Chromosome segregation is mechanically regulated: homologs must attach appropriately and separate to opposite poles. The randomness lies in which valid orientation a homolog pair takes and in the positions and outcomes of recombination events, not in chromosomes being distributed without spindle control.

This distinction is the bridge from cell biology to genetics. Later inheritance units can use independent assortment to derive segregation ratios and use crossover to explain associations between genetic variants on the same chromosome.