Is Shenzhen Xinzhou Women's and Children's Hospital and Futian District Xinzhou Women's and Children's Hospital the same hospital?

It is the same hospital, you can take the bus from Shajing:

m341 road → Longhua line The total distance is about 2 hours / 39.9 kilometers

Shenzhen Shajing Central Bus Terminal 60 meters walk to the Shajing Central Bus Terminal 13 stops to take the m341 road (or 310-315 road), in the Guotai Private City station get off the bus 10 meters walk to the Longsheng station 11 stops to take the Longhua line, in the Fumin station Get off at Fumin Station (Exit D) and walk 120 meters to Futian Maternal and Child Health Center.