TLDR; Fuengirola used to be the port of Mijas so they are really connected. Also prices in Mijas are much lower than Fuengirola and the distance to the city center is really short.
In a daily situation, it's really common that those who live in Mijas refers to Fuengirola as "City Center" or just "The Center". Both places have the same population and we move between places without noticing the difference (in most cases, we don't even know the limits of each)
In a wider scale, Mijas is around 4 times bigger than Fuengirola, what means that you have places like La Cala de Mijas or Entrerríos, where you have to move to Fuengirola by car as there are almost no busses.
In the other side, we have "Calahonda" or "Riviera del Sol", where people is closer to Marbella than Fuengirola so they feel far from a Mijas belonging.
But most of "Mijeños" live in "Las Lagunas", "El Coto", "La Sierrezuela" or "Mijas Pueblo", all those places are really close and connected to Fuengirola, the place where people study, work and party most of the year.
There is also a huge difference between those areas: prices in mijas are much lower than Fuengirola, being much more quite residential areas. In the other side, living in Fuengirola feels much more like a city living than a calmed neighbourhood.