4 cores displayed in Device Manager, Task Manager shows there are 2 cores.



Is this type of processor common for laptops? I once read that i7 are usually 4-core but I now know two laptops that have i7 but really have 2 cores only.

Also does this have a lot worse performance than a same-price Quad-Core?
 

The 2 core i7 mobile version is (totally) different from the 4 core desktop version! And yes, the desktop cversion is faster, but needs a very big cooling system an a lot of power for it - not suitable for laptops though.
 
Like noidea_77 said, if comparing laptop/mobile cpu's to full desktop versions there is a big difference. They're totally different parts for one. The mobile versions are usually clocked slower, have less cores, require much lower power (a large benefit to battery life that's not an issue on desktops), less heat. If comparing 2 core 4 thread (hyperthreaded) to a true quad core, yes the true quad core will be a lot more powerful provided speeds and architectures are similar. A closer comparison since it's a hyperthreaded dual core would be a desktop i3 which is also a dual core hyperthreaded and even then a direct comparison can't be made just based on specs.

There are true 4 core i7's for mobile in the 4th gen but so far all the 5th gen mobile broadwell i7's are 2 core.

http://ark.intel.com/products/family/75023/4th-Generation-Intel-Core-i7-Processors#@Mobile