Speaking from the technology perspective, naming is specific depending on the device characteristics, two main categories being landline and mobile.
Landline is a device receiving signal through a fixed phone line (which is not always a circuit; sometimes the device is a pretty large phone with a SIM making it quite mobile, sometimes handheld, still it's considered a landline phone).
Mobile phones have a couple different technology-dependent types:
- cellular (or cell for short) are called the devices utilizing signal received through a "cellular network"
- satellite devices are powered by the satellite network
These terms describe your device in respect to differences implied by phone networks, but the total of non-landline phones are mobile.
Also there are smartphones. This term distinguishes the device in a bit different dimension; it describes the capabilities as opposed to older handheld devices (smartphones are the devices that combine a microcomputer and a telephone).
So, strictly speaking, if you want to be specific to different types of devies you should use different terms in different cases. That would make a lot of difference if you wanted, per se, sell software for a particular kind of devices.