In our 23 chromosome pairs, do the 2 members of the pair have distinct or virtually identical sequences?
Homologous chromosomes (those that are paired up), excluding the sex pair are almost identical in size, shape and genes (members as you called them) present in them.
Genes determine traits and each homologous chromosome controls the same traits. The level of identity of a gene inside a population varies between genes. There are very conserved ones that do not change even between humans and yeast and others that vary alot event inside a species. This changes can be small in sequence length, a simple base (letter) swap or one deletion, and have a huge effect on the traits. This is how chimps and humans are very different but share 98.6% of their genome and humans are very similar and share 99.9% of their genome.
In summary, on the bigger scale homologous chromosomes are very similar (size, shape, traits inside), on the smaller scale homologous chromosomes have small changes that affect greatly.
EDIT: elaborating on when recombination occurs.
The zygote do not recombine the chromosomes it gets from it's parents. Each parent chromosomes recombine in the first step of meiosis. We do not expect them to be identifcal on the gene level (or the SNPs level). Each chromosome represent each paren't genetic material.
Lets look at parents A chromosomes
parent a Paternal: a-b-c-d-e                       parent b Paternal: a-B-c-D-e
parent a Maternal: a-B-C-D-e                   parent b Maternal: a-b-C-D-e
possible recombination  (a)                       possible recombination (b)
(a-I) a-B-C-d-e                                         (b-I) a-B-C-D-e
(a-II) a-b-c-D-e                                         (b-II) a-b-c-D-e
Now the child can be any of the 4 possible combinations (and obviously all other not shown). Let's say (a-I) and (b-II). This chromosomes do not recombine until they get to the meiosis stage.