Final answer:
Paralogous genes are copies of a gene within the same species that have evolved via duplication, while orthologous genes are genes in different species that have descended from a common ancestral gene and usually retain similar functions.
Step-by-step explanation:
When we say two genes are paralogous, we mean that these genes have evolved by a process known as gene duplication within a single species. This results in a situation where a genome contains two or more copies of a gene. These duplicates can then diverge and may eventually take on new functions. Paralogous genes are often found in the same organism because they originated from a common ancestral gene that was duplicated within the organism's genome.
On the other hand, when we say that two genes are orthologous, we are referring to genes in different species that originated from a common ancestral gene through speciation. Essentially, these genes have separated due to the division of one species into two or more descendant species. Orthologous genes typically retain the same function in the course of evolution.
The study of paralogous and orthologous genes is crucial because it helps us understand the relationships between species and how genes evolve over time to give rise to the diversity of life we see today.