So, in practice, GPS is inevitably A-GPS?
Not necessarily. A-GPS is designed for phones with limited power. The idea is that you embed a smaller chip that can collect ephemeral data and then transmit to an assistance server to do the math required. (The math is what drives up battery consumption). So there are essentially two types – 1) Full blown GPS, does all the computations and 2) The assisted GPS that collects the data and then forwards it to an assistance server for processing.