Are 1uF NP0/C0G capacitors different than regular 1uF capacitors?
No not the same. A 1uF C0G, NP0 capacitor (if you can even find one!) will be very large and expensive (definitely not 0402). The default for a bypass capacitor or similar non-critical application would be something like X7R or X5R but that should be specified. The voltage rating should also be specified. 

C0G, NP0 refers to an EIA Class I dielectric made with very low temperature coefficient and voltage coefficient, typically specified for capacitors in the pF but now easily available up to many nF, however uF levels of capacitance are (today) not easily available. At higher capacitances, dielectrics such as X7R and X5R, X5S and so on EIA Class II diectrics are used because they allow a physically small capacitor to be manufactured inexpensively. 

The designer must work around their many non-ideal characteristics, which include (sometimes extreme) temperature and voltage coefficient (the capacitance may drop by 80% or more at rated voltage) but also microphonics (they tend to generate a voltage from vibration) and aging (the capacitance decreases with time). 

There are also Class III dielectrics such as Z5U but they are significantly more horrible again in characteristics. 

Graph below is from Kemet, a major manufacturer of this type (MLCC = Multilayer Ceramic Capacitors). 



The graph emphasizes the temperature characteristics (and the relative values of the dielectric constants) but the voltage characteristics can be at least as important in design.