The white bordered alpha edition was produced in 1994 and bears 1994 on the copyright line.
The white bordered beta edition was produced in 1995 and bears 1995 on the copyright line.
The sets are otherwise indistinguishable. Additionally there is a silver bordered collector's edition that was distributed in a metal container.
The cards with changes between Alpha and Beta are:
ARMUS - SKIN OF EVIL — changed lore from "Malevolent being formed when the inhabitants of Vagra II rid themselves of all the evil they have inside." to "A malevolent being was formed when the inhabitants of Vagra II rid themselves of all the evil they had inside."
DISTORTION FIELD — changed "prevents any beam down here" to "...prevents beam down/up here..."
EMERGENCY TRANSPORTER ARMBANDS — changed "Beam Personnel up or down at any time, even during a battle before the winner is determined." to "Beam your Personnel up or down at any time, except during a dilemma (unless specifically permitted). May be used during battle before the winner is determined."
EVACUATION — changed "Strength" to "STRENGTH"
FIRESTORM — changed "... unless thermal deflectors present. Discard dilemma." to "...unless thermal deflectors present OR Away Team escapes using emergency transporter armbands. Discard dilemma."
GIUSTI — corrected misspelling of "consol" to "console"
**INVESTIGATE TIME CONTINUUM — corrected misspelling of "Dividia" to "Devidia"
KHITOMER RESEARCH — changed from Romulan to Romulan and Klingon mission
LWAXANNA TROI — corrected misspelling of "Lwaxanna" to "Lwaxana"
MENDON — corrected misspelling of "specialist" to "specialists"
'T'PAN — added MINDMELD skill
THE JUGGLER — corrected misspelling of "Lwaxanna" to "Lwaxana"
TORAL — changed "...bidding of half sisters, Lursa and B'Etor." to "...bidding of Duras's sisters, Lursa and B'Etor."
TSIOLKOVSKY INFECTION — added "(Not cumulative.)"
U.S.S. OBERTH — moved staff icon to center of art block.
WESLEY CRUSHER — removed apostrophe from "Protege' of the Traveler." to read "Protege of the Traveler."
WIND DANCER — corrected misspelling of "Lwaxanna" to "Lwaxana"