The term that describes organisms or genotypes that are homozygous for a specific trait always producing offspring of the same phenotype is true-breeding.

Here's why:

* Homozygous: Means having two identical alleles for a particular trait. For example, a homozygous dominant plant would have two copies of the dominant allele (e.g., AA) while a homozygous recessive plant would have two copies of the recessive allele (e.g., aa).

* True-breeding: Refers to organisms that consistently produce offspring with the same trait when self-fertilized or crossed with another individual of the same genotype. This is because they always pass on the same allele to their offspring.

Example:

Consider a plant with the trait of flower color. A true-breeding plant with purple flowers would have the genotype AA (homozygous dominant). When self-fertilized, it will always produce offspring with the genotype AA, resulting in purple flowers.

In contrast:

* Heterozygous: Organisms with two different alleles for a trait (e.g., Aa) may not always produce offspring with the same phenotype. The offspring's phenotype will depend on the dominant and recessive nature of the alleles involved.

Therefore, the term true-breeding accurately captures the consistent production of offspring with the same phenotype due to the homozygous nature of the parent organisms.