You're right that organisms vary greatly in the number of chromosomes they have. Bacteria all (or at least almost all) have only one chromosome, fruit flies have four pairs, and a plant called the Adder's Tongue Fern(Ophioglossum reticulatum) has over 1,000 chromosome pairs! The number of chromosomes is not what makes an organism genetically unique, though.

Species (and individuals) are unique because of the content of the DNA that makes up the chromosomes, not the number of chromosomes.

As you may already know, chromosomes are made of tightly packed DNA, and DNA is made of incredibly long strands of chemicals called nucleotides. There are four nucleotides, often called "bases" and abbreviated as A, T, G, and C. DNA is unwound and loose most of the time, and it usually only gets tightly packed into a chromosome when a cell divides. (During cell division,the tightly packed chromosome is easier for the cell to move around than along, unwound strand of DNA would be.)

The order of the bases along the strand of DNA, called the "sequence," is the DNA content I mentioned that makes an organism or a species unique. If a one-cell human embryo lost 11 chromosome pairs so only 12 pairs remained, it would not be genetically any closer to a cherry tomato than you are right now. That's because the sequences of its remaining DNA will not have changed, and they don't match the DNA sequences in cherry tomatoes. The change would simply be that a lot of the embryo's DNA sequences were lost(11 chromosome's worth). If you replaced those 11 chromosomes with 11 different chromosomes with different DNA sequences, it would not develop into a normal person, even though it had 23 pairs of chromosomes again.

So it's the DNA sequences, not the chromosome numbers, that make all the difference. Overlap in chromosome numbers do definitely occur. Potatoes and Chimpanzees, for example, both have 24 pairs of chromosomes. Humans are not the only animal with 23 pairs, either--the Chinese subspecies of Muntiacusmuntjac, a small kind of deer, also has 23 pairs of chromosomes.

Are you ready for something really weird, though? A different subspecies of this same deer has only three pairs!

Don't let anyone convince you that the number of chromosomes affects the complexity of the organism, either. It's true that simple bacteria have only one chromosome, but look at these numbers: domestic cats have 19 pairs of chromosomes, and Geometrid Moths have 112 pairs. Moths are definitely not 6 times more complex than cats, even though 6 x 19 equals about 112! And don't forget about the ferns with over 1,000 pairs.

I hope that was helpful and interesting. Keep coming up with great questions!