The glide portion of skating equates to lingering on the LTE of the uphill/inside ski at the very end of a ski turn. (long time span on skates, short time span on skis)
In skating you have to find a state of balance on that glide which lasts much longer then in skiing.
Eventually in skating you move your CoM back inside off the LTE and onto the BTE of that glide skate so that you can do the push off. That equates to the skiing transition of moving the CoM across to the inside of the next turn. In skating that happens by making movements of the inside leg and foot, and by tilting your torso that direction, etc.. These actions pull you onto the BTE of that glide skate and then you can finally do the push off.
The skating push off happens quickly, but equates in skiing to the long held ski glide on the outside ski for the turn. (short time span on skates, long time span on skis)
There are some parallels and what I like the most is awareness of balance, and BTE/LTE edges, what your CoM needs to do on order to be balanced and getting your CoM to the inside for the pushoff, by using inside foot actions.
However, I just want to caution that in terms of timing, the LTE glide on skates is not the same phase as the BTE glide on skis. The gliding portion of skating corresponds to a very short event in skiing, and the glide in skiing equates to short and more muscled push off in skating on the BTE.