Last week I identified sticky prices with a high information transfer index (κ) environment (e.g. Japan since the 1990s or the US now). Effectively, a κ closer to 1 means that P ~ MB^(1/κ -1) → MB^0 ~ 1 and the price level (P) becomes constant under changes in the monetary base (MB). For smaller κ, we get P ~ MB^x with x large; small changes in MB result in large changes in P.  This is one type of stickiness -- relative stickiness. It is dependent on a changing κ so that the response of the price can be considered "sticky" for some values of κ (e.g. ~1) relative to other values of κ (e.g. <<1). You can see the effect of this kind of stickiness in the price level graph:
The the same size changes in the monetary base result in larger movements in the price level in the 1970s versus the 1990s. If κ weren't changing (or there wasn't another κ to compare to), then it would be impossible to say κ was big or small ... big relative to what?
However, there is another type of stickiness I identified in the information transfer model a few months ago. It seems entirely plausible that the labor market could have been described by P1:NGDP→NW, where NW are nominal wages. Shifts in aggregate demand (NGDP) could result in a price signal for workers to lower nominal wages by taking pay cuts, but they don't (in fact, economists tend to puzzle over why this doesn't happen). The price P1 in that market is effectively a constant (~2.1). It's the price P2:NGDP→L where L is the labor supply that detects signals from the aggregate demand, and the labor market responds to recessions by people becoming unemployed rather than taking wage cuts. You can see this in this graph:
The wage market is approximately constant while the labor market is affected by the price level  (this is related to Okun's law). The wage market adjusts to keep NGDP ~ 2.1 NW by workers becoming unemployed an no longer adding their wage to NW. This is a type of absolute stickiness  (as opposed to relative stickiness above) and appears to be indicated by the market for the value of X showing far less response (price elasticity) that the market for the number of X. Essentially, there is always NGDP/2.1 of wages to go around, and the market finds the number of people that make the labor market clear. Other markets tend to work the other way: there are N widgets and the market finds the price that makes the market clear.
So there are (at least) two types of stickiness: relative and absolute. The former is visible in the money market (price level stickiness, i.e. the general stickiness of all prices in an economy) and is path dependent (the monetary base must be large relative to some earlier time) while the latter is visible in the labor market and seems to be invariant over time.
 Note: κ is related to the price elasticities of supply and demand.
 Note: the market P2:NGDP→L is not a perfect fit (green line vs the blue line); there is a small amount of nominal wage flexibility.
 Absolute in this sense doesn't mean prices can't change; i.e. it doesn't mean infinitely sticky, but rather sticky without reference to another price (or at different time).