Short run versus long run in cointegration

#1
In dealing with cointegration there are discussion of short term (error correction) models and long term effects (the cointegration). But I have yet to find a description of what this means in practice even when slopes are generated. What is the practical ramifications of short and long term effects in dealing with cointegration/error correction models.

An example of what this means (not an answer to my question)

"To capture the long‐ and short‐term causal relationships between crude oil price, energy consumption and CO2 emissions in Ecuador from the log‐linear equations specified in models 1 and 2, this study employs the autoregressive distributed lag testing approach to cointegration (ARDL‐bounds) of Pesaran et al. ([ 32] ) incorporating the structural break observed in the data series. The ARDL approach is considered to offer several desirable statistical features that overcome the limitations of other cointegration techniques (Pesaran et al., [ 32] ) and has become increasingly popular among researchers in recent years (Jayaraman and Choong, [ 14] )."

https://web.a.ebscohost.com/ehost/d...zdC1saXZlJnNjb3BlPXNpdGU=#AN=125349877&db=aph

the link probably won't work for anyone.
 
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#2
While I am at it, how do you test the differences in an ADF test. As compared to the raw data? Subtract one point from another and test that?

"The ADF tests (see Table 1) demonstrate that all of the variables, save unemployment, were nonstationary in levels but stationary in differences, i.e., were I(1) variables."