And the difference in practice is???
When the privilege of the writ was suspended, new writs of habeas corpus could still be petitioned, but the privilege of courts acting on the writs was suspended. If the writ itself were suspended, then no new writ petitions could be filed, and prisoners would lack the legal recourse of the writ. The difference in practice would be the total amount of time needed for someone arrested to have a petition be filed with, processed by, and acted upon by a court.