We state as an objective extending democracy throughout the world but you are correct.
Correct.
The difference is that in a true democracy issues are decided by a direct vote of the people. In a democratic republic they are decided by representatives of the people.
Correct.
And in some countries, the people have NO SAY, NO VOTE.
And in some countries, they remain that way, or thereafter elect representatives, or choose a direct VOTE of the people to be counted and the election results are by direct vote (known as a populous vote).
This is a minor point and has nothing to do with the Democratic and Republican parties.
Actually it does, because BOTH parties promote a representative voting system throughout the world.
BOTH parties promote EQUALITY ~ "under the law". Which is to say, regardless of the individual, every individual is TREATED the SAME, in legal matters. (ie, "under the law")
And further ~ each party promotes their own agenda, at home and abroad, which outside of the frame-work of "VOTING", are extremely different agenda's.
Republicans promote individual Liberty.
Democrats promote Socialism.
Socialism is a system whereby the Government owns and controls everything, and equally doles out to the People at large.
Liberty is an ideal (and premise upon which this country was established) whereby everyone is an individual to excel in whatever they choose to gain intelligence, wealth, property, etc. and manage it themselves, or not.
And for the most part, many people do not know the difference, but rather support the "PARTY" who promises to "TAKE CARE OF THEM", ie, lumps who do not plan, desire, exert the effort or want to take care of themselves; ie socialists.