Yes and no. Servicemen, service members, etc. are a bit more general, and typically refer to someone in the military, in whichever branch, be it Army, Navy, Marines, Coast Guard, Air Force... soldier is a term specific to the Army.
Over 500,000 US servicemen were in country in 1968/69. Servicemen, counts US Soldiers, Coast Guardsmen, Sailors, Airmen, and US Marines.
Over 1,100 British servicemen were killed.
For the US, over 58,000 servicemen died. For Australia, approximately 600 servicemen died.
US Servicemen are still missing in action (unaccounted for).
Approximately 2,594,000 US Servicemen served in the Vietnam War.
Anti-war sentiment lowered the morale of the US servicemen.
16,353,700 United States servicemen served in World War Two.
GI Bill of Rights
Over 3,000 Australian Servicemen wounded in Vietnam.
Over 400,000 US servicemen were killed in WW2.
Badly by most civilians, treated as brothers by their fellow servicemen.
24 NZ servicemen have won the Victoria Cross. :)