When the Spanish Civil War broke out in 1936, the Nationalist forces immediately began using the form the Spanish State rather than the Spanish Republic or the Spanish Monarchy, out of deference to the differing political sensibilities of the members of the Nationalist coalition, which included the fascistic Falangists and the rival monarchist parties the Carlist and the Legitimists.
The Spanish State was declared a monarchy in 1947, but no king was designated; the Chief of State, Franco, reserved for himself the right to name the person to be king, and deliberately delayed the selection due to political considerations. The selection finally came in 1969, with the designation of Juan Carlos de Borbón as Franco's official successor (this selection was an unpleasant surprise for many interested parties, as Juan Carlos was the rightful heir for neither the Carlists nor the Legitimists).
With the death of Franco and the dismantling of the Franquist régime, the Spanish State ceased to exist, being thoroughly reconstituted as a constitutional monarchy, where the head of state reigns, but does not rule.
"Estado Español" and its translations is still used by nationalists who don't acknowledge Spain as a real nation, but as a state currently holding several nations. Thus, in this usage, a empresa estatal ("State business") means just a Spanish business , not necessarily state-owned. And the Spanish football team may be called selección estatal.