The main difference between a standard projector and a mini projector is that traditional projectors are designed to produce the highest possible quality at the most significant possible size, and if that means more giant bulbs or LED assemblies and louder fans, then so be it. Mini projectors also deliver good quality, but their priorities are different: they're also designed with portability and price in mind, so they're often more portable and affordable than their bigger siblings and often include built-in speakers and easy Bluetooth speaker connectivity.
Standard projectors are mainly powered, but many mini projectors are also designed to run on battery power. Like any battery-powered device, they have limited running times compared to when they're plugged in, but most models have more than enough power to show multiple movies without requiring a recharge halfway through. It can also mean that the projector is dimmer than a wired one to get more life out of the battery.
The other key difference is that mini projectors are designed to be set up speedily, and that can mean they have fewer connection options than wired models. However, the growing adoption of wireless technologies such as Google Cast and AirPlay and intelligent TV-style features such as streaming apps that work over Wi-Fi means that many mini projectors can get video from many sources.