Hi @sugata_hisato,
The difference is in how coherence is estimated, this is a detailed description of the two methods:
A. Connectivity > Coherence [2021] > Lagged Coherence
This process obtains only one coherence spectrum estimate using all the windows
These 2 parameters control how coherence is computed:

Time window: This refers to the part of the signal that you want to analyze, often All file is often selected.

Window length for PSD estimation: Time window to compute the xyCrossSpectrum, and the x yAutoSpectra (which are the same to their PSDs). These spectra are used to compute coherence. Overlap for PSD estimation: This parameter controls the number of windows that will be used to estimate the coherence spectra in the current segment.
Coherence (C
) is computed as the ratio of the xyCrossSpectrum, and the x yAutoSpectra
For example with these parameters:
 Time window: 0 10,000 ms
 Lagged coherence
 Window length for PSD estimation: 2000 ms
 Overlap for PSD estimation: 50% (250 ms)
If the input is one file, and Output option is Save individual results... :
 The first 10 s of signal are split in 9 windows of 2 s, with 1 s overlap. One xyCrossSpectrum, and two AutoSpectra (one for x and one for y) are computed for each window.
 Then, xyCrossSpectrum, and two AutoSpectra are averaged across windows.
 The Coherence spectrum is computed using the averaged CrossSpectrum and averaged AutoSpectra. Thus there is one Coherence spectra for the 10s signal
4.Finally, lagged coherence is then computed from C
as LC = imag(C) / sqrt(1  real(C)^2)
If the input are multiple files, and Output option is Average crossspectra..., one Coherence spectrum is obtained from the averaged (across all windows in all files) xyCrossSpectrum and AutoSpectra
B. Connectivity > Envelop correlation [2022] > Lagged Coherence
Computing coherence through the "envelope correlation" process, is a bit different, as there is one coherence spectrum estimate for each window
These 3 parameters control how coherence is computed:

Time window: This refers to the part of the signal that you want to analyze, often All file is often selected.

Time resolution:
 Dynamic (one coherence estimate per window)
 Static (average coherence spectrum across windows)

Estimation window length: Time window to compute the xyCrossSpectrum, and the x yAutoSpectra (from the TF representations). Sliding window overlap: This parameter controls the number of windows.
Coherence (C
) is computed as the ratio of the xyCrossSpectrum, and the x yAutoSpectra
For example with these parameters:
 Time window: 0 10,000 ms
 Morlet wavelet: 1:1:40 Hz
 Lagged coherence
 Time resolution: Dynamic
 Estimation window length 2000 ms
 Sliding window overlap 50% (1000 ms)
If the input is one file, and Output option is Save individual results... :
 A TF representation is obtained using the Morlet wavelet approach (40 frequencies)
 The TF map is then split in nine windows of 2 seconds each, with 1 second overlap
 For each window, CrossSpectrum and AutoSpectra are computed using all the time samples in the window (nTimeSamples = estimation_window_length * fs)
 Then a Coherence spectrum is computed for each window, thus there are a total of nine Coherence spectra for the 10s signal
5.Finally, lagged coherence is then computed from C
as LC = imag(C) / sqrt(1  real(C)^2)
Note: The Static time resolution option performs the average of the lagged coherence, and not the average of the CrossSpectrum and AutoSpectra (as it is done in Coherence [2021])
If the input are multiple files, and Output option is Average crossspectra..., the previous steps are executed for each file, and the result is averaged across files.
Best,
Raymundo