Universal, cosmic, ecumenical, catholic, cosmopolitan can all mean worldwide or at least extremely widespread (as in extent, range, influence, appeal, or use).
Universal is likely to suggest what is worldwide rather than pertinent to or characteristic of the whole universe; it is often further narrowed to refer to the world of men and human affairs or to important or significant parts of this world. It is likely to indicate a unanimity or conformity of practice or belief or a broad comprehensiveness <no other theory which has won universal acceptance —Binyon > <the universal favor with which the New Testament is outwardly received —Thoreau > <replaced a philosophy which was crude and raw and provincial by one which was, in comparison, catholic, civilized, and universal —T. S. Eliot >
Cosmic is used to suggest matters pertinent to the whole universe as opposed to the earth, especially in suggestions of infinite vastness, distance, or force <sardonic phantoms, whose vision is cosmic , not terrestrial —Lowes > <the great cosmic rhythm of the spirit which sets the currents of life in motion —Binyon >
Ecumenical applies to situations involving people throughout the whole world or all people in groups or divisions as indicated, often in religious contexts.
Catholic may stress an attitude involved, as well as a fact, in the including, comprehending, or appreciating of all or many peoples, places, or periods.
Cosmopolitan may imply an understanding and appreciation of other lands, sections, nations, or cities coming about through personal experience in traveling or living elsewhere; it often contrasts with provincial .