Transmitters
No, there are more than 850, 880, and 940nm transmitters: the IR spectrum ranges from 700nm to 1mm. A distinct set of values is sold, typically in the 700 to 1400 nm range (IR-A), where 850, 880, and 940 are common values. Here's a selection of the Mouser listing of IR emitters. I've used the TSAL series of emitters from Vishay, although I'm not sure that they're in your current, brightness, or bandwidth specs.
The parameter you're interested in for transmitters is the "Relative Radiant Power vs. Wavelength", and for receivers, you want to know the "Relative Spectral Sensitivity vs. Wavelength". For instance, the bell curve in Fig. 9 of the datasheet for the TSAL6100 shows that it has a relative intensity of 1 at 940nm, and outputs about 0.125 times this intensity at 890 nm. That likely means that it's not bright enough to use with an 850 nm detector, and would be iffy at best with an 880nm detector.
Receivers
On the plus side, receivers are usually more generous, for example the TSOP348 detector [picked at random] has a spectral sensitivity of better than 80% for all wavelengths between 850 and 1050nm. Taos Inc. also makes some nice digital, analog, and frequency output detectors for many wavelengths; I've used them with good success before. This will help you if you need to replace a sensor, especially if it's just used as an on/off digital sensor, for instance in a light curtain application, because 80% is pretty close to 100%.
However, that sort of receiver will only tell you about the quantity of light. If you knew that your LEDs were the same brightness (you don't), then you might be able to infer a frequency (i.e. this one is 75% as bright as the 950nm, therefore it's about 820 or 1070nm). You can also determine that an LED is on with just a digital camera, like the one in your cell phone.
Color Sensors
An infrared camera could tell you the wavelength after compensating for temperature, but would not fit most budgets. (Note: These are awesome for determining all kinds of things - Night vision, temperature gradients, etc.)
What you need for that is an color sensor in the infrared range. A color sensor will have multiple narrow-band and/or filtered detectors, so that you can determine the color of the light. See Figure 1, Photodiode Spectral Responsivity" of the datasheet for the TAOS TCS3200D[pdf] for an example (No, it's not going to be a pretty algorithm...). However, you'll notice that the visible light filters stop at about 750nm, and everything goes back to the same curve. Finding a color sensor that works into the infrared range is left as an exercise to the reader, but this sort of IC is what you're looking for.
An alternative to an IR color sensor (which may not exist) would be to use a broadband sensor with a set of infrared transmitting filters tuned to the region of the spectrum which you need. A quick Google search turned up this page, you'll probably find something better.
Distributors:
As for distributors, I find that Mouser has a better selection and cheaper prices on optoelectronics than Digikey.
What you are asking is how flat the spectrum of various light measuring devices is. Good devices of either type will have datasheets that tell you this. Usually there is something called a "spectral sensitivity" graph.
If I remember right, photodiodes have narrower spectral sensitivity than CdS cells in general, but can be made to different center wavelengths. For example, 980nm is a common wavelength for IR detectors.
One way of getting a flat spectrum is to use multiple sensors, each peaking at a different wavelength or with a different filter in front of them. Software then uses the various values to compute the "flat equivalent" intensity.
Best Answer
You can hardly think of anything simpler than a photodiode or phototransistor: place a series resistor and you have a voltage proportional to light level. The resistor's value sets the sensitivity. In the past I've used the SFH3410 for this several times.
You want a phototransistor with a eye-matched sensitivity curve. Most phototransistors are rated for a limited light range, like the SFH3410, which is only specified between 10 lux and 1000 lux. I've used it for levels down to 1 lux as well, and it was still linear at that level.
For higher levels (direct sunlight in summer can go beyond 100 000 lux) I would suggest to use a second phototransistor where you place an ND (neutral density) filter in front of it. A 99 % filter will reduce the 100 000 lux to 1000 lux, so you can measure the higher light levels with the second phototransistor.