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While creating stream network, I implement a thresholding. All cells's value is "1". Later, while creating stream segments, Do I use the second thresholding for separating link to segments ?

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To create the raster stream network you first threshold a flow accumulation raster, likely using the Raster Calculator or the Con tool. You're right that this will create a Boolean streams map of 1's and 0's. To break the streams raster into the various stream segments (links or tributaries) you would use the Stream Link tool using the same streams raster generated from the first thresholding as the input. The Stream Order tool will also take the same raster stream network derived from the first thresholding operation. So, for any stream network analysis that you perform on a DEM-derived stream network, once you've settled on the the threshold using the techniques described in this answer, you don't change the threshold for subsequent analysis operations.

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To separate into segments, use the stream link tool

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