“the boat.” This would have been the boat that he had come over on (cp. Mark 5:18). It seems most likely that Jesus would have gotten into the same boat he came in, and the Gospel of Mark says, “the boat.” Also, many Greek manuscripts read “the boat” here in Matthew 9:1.
“the lake.” The “sea” of Galilee is actually quite a small lake, only 7 miles (11.2 km) across and 12 miles (19.3 km) long, and the entire lake can be seen from the escarpments on both the east and west sides. The Greek word thalasso, lake, sea, or ocean, does not really refer to the size of the body of water, and thus has to be translated into the English “lake,” “sea,” or “ocean” by knowing the body of water that is being referred to (see commentary on Matt. 4:18).
“his own city.” Capernaum. Jesus moved to Capernaum after the people of his hometown, Nazareth, tried to kill him (Luke 4:29-31; cp. Matt. 4:13). Jesus either bought or rented a house in Capernaum, because John 2:12 indicates he even moved his family there. As we see in this verse, Capernaum became known as Jesus’ “own city.” One of the reasons Jesus likely picked to move to Capernaum was that it was on the Via Maris, the Road of the Sea, which was the great trade route from Egypt in the south to Damascus in Syria and on to Mesopotamia (see commentary on Matt. 4:15).
[For more about Capernaum being Jesus’ hometown, see commentary on Mark 2:1.]