What you are looking at are the current NYC Planning Board maps that are found on the internet. The defined areas are the administrative areas and not operational/response areas. There is a difference between the two types of areas.
If we look at the East Bronx, Eng 90 & Lad 41 are in the 20th Batt administrative chain of command. However part of their 1st due area and 1st alarm response area has both companies companies responding with the 18th Battalion besides Batt 20. First due area is defined as locations where the first unit is planned to be the first arriving engine or ladder. First alarm response area is where an engine company is normally scheduled to either arrive first, second, third, or forth due, For a ladder company only first & second due box locations are considered to be the first alarm area.
Another good example is Battalion 19. First of all they are not responsible for Woodlawn, Batt 15 has that area for both administrative and response.
But did you know that years back Battalion 19 was in Manhattan's 5th Division long after Division 5 relocated back to Manhattan?
So when you look back in FDNY history at the start of the 1950's there was only 6 battalions within the Bronx. Battalions 14, 15, 17, 18, 19, & 20th.
At that time Battalion 19 was composed of Engines 43, 52, 68, 75, 81 and Ladders 33, 46, 49, & 52.
Batt 14 had Eng 41, 60, 73, & 83 with Lad 17, 29, & 42 (Res 3 was at Lad 17)
Batt 15 had Eng 38, 62, 63, 79, & 97 with Lad 32, 37, 39, & 51.
Batt 17 had Eng 50, 71, 82, 92, & 94 with Lad 19, 31, 44, & 48.
Batt 18 had Eng 42, 45, 46, 48, 88, & 96 with Lad 27 & 38.
Batt 20 had Eng 61, 64, 70, 89, & 90 with Lad 41, 47, 50, & 53.
When the 3rd Battalion was re-established they were assigned to the Bronx causing a reorganization or realignment of fire companies.
Back in 1959 the re-alignment of Bronx fire Battalions & Companies end up as:
Batt 3 = Eng 50, 82, & 94 Lad 19, 31, & 48
Batt 14 = Eng 41, 60, 73, & 83 Lad 17, 29, & 42
Batt 15 = Eng 38, 62, 63, 79, & 97 Lad 32, 37, 39, & 51
Batt 17 = Eng 42, 68, 71, & 92 Lad 44 & 49
Batt 18 = Eng 45, 46, 48, 88, & 95 Lad 27 & 38
Batt 19 = Eng 43, 52, 75 & 81 Lad 33, 46 & 52
Today Battalion 19 is composed of Eng 42, 43, 75, & 81 Lad 33, 46, & 59.
The reason why Batt 27 shows having two areas is because the decision the department made to split up the North Bronx when Batt 27 was relocated from Eng 82 to Eng 79. Give consideration that Batt 15 also moved from Eng 62 to Eng 63's qtrs. Consideration not only for fire duty but also administrative duties is also reviewed.
So today Batt 27 has Eng 52, 62, & 79 Lad 32, 37, & 52.