Why does ethylamine have two infra-red spectra? Are both correct?
When looking at IR spectra of hydrogen-bonding groups, always check how IR spectra was recorded. It appears that NIST spectra is recorded using gas phase, while the first one used liquid film. In liquid film $\ce{NH2}$ groups form a network of hydrogen bonds, resulting in shape distortion and widening of $\ce{NH2}$-related bands. Same is true for carboxylic acids, alcohols, phenols, and many other group.  Comparison of water spectra in ice, liquid and gas is particularly enlightening.
If the spectrum is recorded in a solution, you also have overlapping spectrum of the solvent in your recording. If you look at water spectrum in liquid phase (nist webbook), you can see some wide peaks suspiciously similar to wide bands in the first spectrum you posted, so it might be that 'liquid film' is actually a water solution. In this case the situation is even worse, because in addition to ethyl amine spectrum you also have overlapping ethyl ammonium spectra.