This has been explained 1000's of time before. I'll try again here to explain the difference in pressure readings. Others will correct mistakes I might make
You already understand "raw" pressure. This is also called "station pressure".
What if you are a weatherman and want to draw a chart of pressure covering say all of Oregon? Your goal is to analyse varying pressure due to weather systems moving through your state. You have pressure reports from elevations at sea level to well over 10,000 feet. If you draw this chart using station pressure it will be distorted by the different elevations of the reporting stations. That's what sea level pressure is for. You adjust high elevation station reports to what they might read if the station was at sea level. The actual process is quite complicated and not always all that accurate. In fact there are several different ways to do the calculation which yield slightly different results. You need to know temperature, station pressure, altitude and for some conversion techniques, special correction factors specific to your location. Yuck.
Altimeter settings are for airplanes. The altimeter in an airplane is a glorified barometer, calibrated to read altitude instead of pressure. However, due to several non-ideal factors it will not read altitude accurately unless it is adjusted to account for local atmospheric conditions. That means pilots must periodically re-adjust their altimiters as they fly to keep up with changes in local conditions. Pilots just get a new setting on the radio, then turn a knob on the altimeter to accomplish this. Numerically, the conversion between station pressure and altimeter setting is much simpler than for sea level pressure, and there's only one formula -- not several different ones as with SLP.
The difference between altimeter and SLP values depends on several things, but primarily station pressure, temperature and altitude. At low elevations the differences are not all that great, but at elevations above 1000 feet they can be significant. If you live in Colorado at 5000 feet for example these differences can be rather large.
So, what is the problem with Davis?. Internally they measure station pressure. Then they perform their chosen version of the calculation to sea level pressure and then give you the result -- but you are not given access to the raw pressure level. (IMHO it is silly for a top-end outfit like Davis not to give you station pressure -- but they don't and all you can do is complain.)
CWOP wants altimeter setting because it is then easy for them to convert back to station pressure as they also know your altitude. But then, why don't they just ask for station pressure directly? You'd have to ask them...I'm clueless on that.
So given the Davis SLP reports, you need to first convert back to station pressure (that's the really hard part), then to altimeter for CWOP. I'm not familiar with WeatherLink...perhaps someone else can explain how to do this conversion with WeatherLink? Or if it is even possible? I'm just trying to help you understand the different ways that pressure is reported.
You could try subscribing to the CWOP mailing list and asking the question there -- if there's an answer, the folks there would know.
In summary, you should blame the complexity of barometer units on weathermen and pilots. Not that it would help...but you might feel better!