There are three main categories of classifying tomato cultivars. Two are somewhat related, kind of like second cousins, and the other is not.
Open Pollinated
Do you have a family member, perhaps a grandparent, that grows the same type of tomatoes year after year? Maybe they save their own seed and replant those seeds the next year? This is at the core of Open Pollinated tomatoes. When you grow tomatoes near each other, and save the seeds from them year after year, without regard to cross-pollination, you end up with an Open Pollinated variety. Indeed, the name "Open Pollinated" suggests that no particular care is placed on how pollination occurs. In many plant varieties, the wind takes care of this. However, in the domesticated Tomato, wind alone is not very likely to cause one tomato to cross-pollinate another. Usually, tomatoes pollinate themselves, with an occasional cross pollination coming from bees visiting multiple plants in the garden.
The issue here is that the domesticated tomato has been bred (probably not on purpose), so that it's not as "promiscuous" as its wild cousins. The stigma of the flower barely is usually protected by the anther cones so that it cannot receive wind-blown pollen from nearby tomatoes. Here are two shots of tomato flowers. The first image is a typical domesticated tomato flower, where the stigma is inserted, while the second image is from a tomato from Joseph Lofthouse with an exerted stigma
So with Open Pollinated varieties, the source of your seed has selected what was likely a stable cultivar over several generations.
With Open Pollinated varieties, if you save seed from the fruits and grow them out the next year, the plants will almost always be very similar to the ones from which the seeds were saved.
Heirlooms
Heirlooms are varieties that were selected as Open Pollinated varieties, but passed down from generation to generation amongst humans. All Heirlooms are open pollinated, but not all open pollinated varieties are heirlooms. The main distinction here is that these are typically varieties where the same seed was grown, and saved, year after year, by an individual or family over several decades.
Hybrids
Have you ever browsed seed catalogs and spotted a "F1" moniker next to a variety? Perhaps it was outright called a hybrid? The "F" in the "F1" stands for "Filial Generation", and the number represents which Filial Generation. A F1 represents the first filial generation of a crossing of two stable parental lineages.
Merriam Webster defines "Filial Generation" as:
a generation in a breeding experiment that is successive to a mating between parents of two distinctively different but usually relatively pure genotypes
A hybrid is usually the offspring of two distinct Open Pollinated varieties, where each parent has a fairly stable lineage. When those two parents are crossed, they produce offspring that are fairly consistent themselves. However, if one were to save seed from a hybrid and grow it out, it would not be representative of the parent plant from which the seed was obtained.
So what happens if you save seed from a Hybrid and grow it out - you just said it won't be representative of the parent plant? That's right. Whereas saved seed from an open pollinated variety will almost always produce plants that are very similar to the parent, saved seeds from a hybrid will produce wildly different results. Absence of mutations, the offspring will resemble one grand parent or another, or some combination thereof - but it's unlikely it will be true-to-form to its parent.
Open Pollinated
Do you have a family member, perhaps a grandparent, that grows the same type of tomatoes year after year? Maybe they save their own seed and replant those seeds the next year? This is at the core of Open Pollinated tomatoes. When you grow tomatoes near each other, and save the seeds from them year after year, without regard to cross-pollination, you end up with an Open Pollinated variety. Indeed, the name "Open Pollinated" suggests that no particular care is placed on how pollination occurs. In many plant varieties, the wind takes care of this. However, in the domesticated Tomato, wind alone is not very likely to cause one tomato to cross-pollinate another. Usually, tomatoes pollinate themselves, with an occasional cross pollination coming from bees visiting multiple plants in the garden.
The issue here is that the domesticated tomato has been bred (probably not on purpose), so that it's not as "promiscuous" as its wild cousins. The stigma of the flower barely is usually protected by the anther cones so that it cannot receive wind-blown pollen from nearby tomatoes. Here are two shots of tomato flowers. The first image is a typical domesticated tomato flower, where the stigma is inserted, while the second image is from a tomato from Joseph Lofthouse with an exerted stigma
So with Open Pollinated varieties, the source of your seed has selected what was likely a stable cultivar over several generations.
With Open Pollinated varieties, if you save seed from the fruits and grow them out the next year, the plants will almost always be very similar to the ones from which the seeds were saved.
Heirlooms
Heirlooms are varieties that were selected as Open Pollinated varieties, but passed down from generation to generation amongst humans. All Heirlooms are open pollinated, but not all open pollinated varieties are heirlooms. The main distinction here is that these are typically varieties where the same seed was grown, and saved, year after year, by an individual or family over several decades.
Hybrids
Have you ever browsed seed catalogs and spotted a "F1" moniker next to a variety? Perhaps it was outright called a hybrid? The "F" in the "F1" stands for "Filial Generation", and the number represents which Filial Generation. A F1 represents the first filial generation of a crossing of two stable parental lineages.
Merriam Webster defines "Filial Generation" as:
a generation in a breeding experiment that is successive to a mating between parents of two distinctively different but usually relatively pure genotypes
A hybrid is usually the offspring of two distinct Open Pollinated varieties, where each parent has a fairly stable lineage. When those two parents are crossed, they produce offspring that are fairly consistent themselves. However, if one were to save seed from a hybrid and grow it out, it would not be representative of the parent plant from which the seed was obtained.
So what happens if you save seed from a Hybrid and grow it out - you just said it won't be representative of the parent plant? That's right. Whereas saved seed from an open pollinated variety will almost always produce plants that are very similar to the parent, saved seeds from a hybrid will produce wildly different results. Absence of mutations, the offspring will resemble one grand parent or another, or some combination thereof - but it's unlikely it will be true-to-form to its parent.