The i3 2310m and i3 380m are more or less the same; the i3 380m will be marginally faster.
The biggest difference is the graphics core. The i3 380m will be paired with an Intel GMA 4500 graphic core in budget laptops. More expensive laptops can have dedicated graphics cards like the nVidia GT 560. The i3 2310m includes a graphics core inside the CPU called the Intel HD 3000. It give 2x more performance than the GMA 4500 in games. In fact it is marginally faster than the desktop Radeon HD 5450. Of course more expensive laptops with the i3 2310m can also have a dedicated graphics card as well.
Not that it make much of a difference for most people, but the i3 380m can only recognize 8GB of RAM while the i3 2310m can recognize up to 16GB. Since most laptops only have two memory slot and 8GB sticks of RAM are really expensive, most people will not install that much RAM in a laptop.