The yellow 'Cavendish' bananas found in grocers around the world are triploid cultivars. They are parthenocarpic (fruit without any fertilization) and sterile. Propagation is by cuttings (cloning). This makes them susceptible to disease (no genetic variation and no breeding is possible), and slowly the world's banana plantations are dieing out. The 'Cavendish' will probably be a thing of the past within my lifetime. This has already happened to the previous mass-produced cultivar (Gros Michel) which is not extinct but is rarely grown due to fungus problems.
Yes wild bananas and plantains with viable seed have large seeds. The black bits in mass-produced cultivars are the remains of the seeds but are completely sterile.
Stores and markets in tropical regions typically have a wider range of banana varietes and you may find ones which are not sterile. As well as the seed making them harder to eat, "wild" varieties tend to have a lot more flavor but do not travel very well.
The development of new banana cultivars that are disease resistant but still suitable for long distance transport is an area of active research. It is an application where a case can be made for modern genetic engineering over traditional propagation techniques.