Good morning Ivan,
You have asked about the Torrance area zip codes that are truly different and will produce completely different results for your family. 90502 is located in Torrance P.O. an area that is mostly part of the unincorporated neighborhood of LA County. It carries the Torrance name only because the Torrance area Post Offices service it. 90503 is West Torrance and part of the city of Torrance. Utilizing the services offered by the City of Torrance (schools, police, fire etc). The rental options will be different for you and your budget. Feel free to contact me to discuss what I can do for you and your budget options.