Yes they are all related to the corn that originated here in the Americas that was cultivated by the Natives for thousands of years. Stock was sent to Asia in the form of corn kernels.
There are specific cultivars of baby corn grown in Asia for example. There are some varieties of baby corn available for seeding here in the US. However, the baby corns can be picked from sweet corn, field corn, proclaimed baby corn cultivars and , even pop corn with out a depreciation in quality among them.
All you have to do is collect the tiny ears of corn within two days of corn silk emergence from any of the above listed corns. The sugars haven't begun to form so they all taste the same. If you wish to get the mature corn later, to eat, To feed the the animals or use as seed leave the top ears on and pick off the bottom one.