First, understand that the Intel desktop processor designation is very different from their mobile processor designation.
Desktop:
i7 = 4 cores, hyperthreading (8 virtual cores), turbo boost, 8 MB cache
i5 = 4 cores, NO hyperthreading, turbo boost, 6 MB cache
i3 = 2 cores, hyperthreading (4 virtual cores), turbo boost, 3 MB cache
pent = 2 cores, NO hyperthreading, NO turbo boost, 3 MB cache
cel = 1 or 2 cores, NO hyperthreading, NO turbo boost, 1-2 MB cache
Laptop:
i7 = 2 or 4 cores, hyperthreading (4 or 8 virtual cores), turbo boost, cache 4MB (dual) 6-8 MB (quad)
i5 = 2 cores, hyperthreading (4 virtual cores), turbo boost, 3 MB cache
i3 = 2 cores, hyperthreading (4 virtual cores), NO turbo boost, 3 MB cache
pent = 2 cores, NO hyperthreading, NO turbo boost, 2 MB cache
cel = 2 cores, NO hyperthreading, NO turbo boost, 2 MB cache
Cache sizes have changed a bit with Haswell, and there are small variances for specific models. Check the specific processor to be sure they fit the above norms.
http://en.wikipedia.org/wiki/List_of_Intel_Core_i7_microprocessors
http://en.wikipedia.org/wiki/List_of_Intel_Core_i5_microprocessors
http://en.wikipedia.org/wiki/List_of_Intel_Core_i3_microprocessors
http://en.wikipedia.org/wiki/List_of_Intel_Pentium_microprocessors
http://en.wikipedia.org/wiki/List_of_Intel_Celeron_microprocessors
The most significant difference between a mobile and desktop version is the i5. On the desktop it's a quad core, on laptops it's a dual core. In fact, for all intents and purposes, a mobile i5 is just a mobile i3 with turbo boost (the i5 also supports TXt, vPro, and VT-d - if you don't know what these are you don't need them). This is very different from the desktop where the i5 gets you twice the physical cores and cache of an i3.
As best as I can tell, the only difference between mobile pentiums and celerons is the clock speed. Compared to the i3-i7, both use older versions of integrated graphics (first gen HD graphics, instead of HD 4000+).
I'm not as up to speed on AMD processors. Just that the E-series was their previous line and only really suitable for netbooks. Their current line is the A-series (A4, A6, A8, A10, just like Audi). While these lag badly behind Intel in CPU performance (the quad core A8 and A10 can barely keep up with a dual core i3), they're paired with fairly strong GPUs. So they may be a better choice if you plan to do 3D gaming on integrated graphics.