When measuring noise you precede your instrument with a filter so you are sure over what bandwidth the noise in being measured. Take for instance a video circuit, it is specified to be flat to 5MHZ. so you hook your noise measuring set to it and actually measure a significant carrier at 8MHZ (clock breakthrough from some where). Its not in the band of interest so it should be filtered out, so you precede the noise measuring set with a 5MHZ low pass filter. An interesting bit of the video band is 4.4MHZ +- 1MHz, this is where the chrominance channel is on PAL TV, any noise in this band would show up badly on the coloured bits of a picture. So you precede the noise measuring set with a suitable filter ( "chroma filter"), else your wideband measurements won't tell you much about the noise in the colour area. Also for audio the filter is not only band- limited but also so weighted, as the ear is much more sensitive to the frequencies around 2Kz, then 20Hz or 20KHz.
As to your particular case, you have thermal noise generated by both the LED and resistor (in parallel) and shot noise due to the LED. Look at Wikipedia.org for explanations.
Frank