There are actually about a dozen political parties in the USA. They sometimes have the same candidates nominated for Pres/VP. I.E. in 2016 the Socialist Party in the USA had Bernie Sanders for pres. In addition to Socialist Party, some others are: Green Party, Libertarian party, Labor Party, and various off-shoots of the Republicans and Democrats. Each party needs to acquire the necessary number of signatures on a petition in each state in order for their candidate to be listed on the ballot for that state's presidential election.
Candidates are elected by popular vote by state. So for instance in 2016, when 2/3 of CA's 9 million votes went for Hillary Clinton, then Hillary Clinton received all 55 electoral votes for president (the same number of representatives CA had in the house in 2016). However, even if she had received only 4.5 mil + 1 of the 9 mil votes, she still would have received all 55 electoral college votes.
This is why each state in the USA lobbies so hard to determine their population because it determines how many representatives they get in the House of Representatives and their impact on the Presidential election. As a comparison, Iowa has a total population just over 3 mil and has only 6 electoral votes and representatives in the house. So in order to overcome CA's voting power for president, another candidate would need to win 10 more states the size of Iowa just to overcome CA. That is basically how Trump won in 2016. Hillary won the most populous states, but Trump won the majority of states. He ended up with the Electoral College win. Hillary could have won all 9 million votes in CA and Trump zero, she would still only receive 55 electoral votes from CA. I say that because if you remove CA from the equation in 2016, Trump won the popular vote as well as the electoral college.
CA (42 mil population) is almost twice as populous as either NY or FL. Using just those three states, if candidate 1 running for president won CA (53 votes in 2020) and candidate 2 won both TX (27) and FL (27,) then candidate 2 would win the electoral college by 1 vote.
Today, the only way the media will give a non-Rep/Dem candidate the time of day is if they can gain around 5 or 6% of the polls early in an election year. However, the only way you can get that much attention is if the press will cover your candidate. So unless you're Joe Moneybags as an independent it is near impossible to ever make it onto a debate stage. This is why Bernie Sanders (Independent) keeps running as a Democrat. He knows he wouldn't get the time of day otherwise.
History lesson for those who care:
When Abraham Lincoln was elected president in 1860 there were four candidates running for President. Three of them were from various Democratic Parties. Lincoln was from the newly formed Republican party, which was anti-slavery. The Republican party was so new (and not popular in the southern states) that Lincoln did not gain enough signatures to even show up on the ballot for president in seven southern states. Lincoln finished dead last of the four candidates in another three states (all slave-owning). Lincoln easily won the electoral college and popular vote in a land-slide (Lincoln's totals were greater than the other three candidates added together). So you can imagine the shock of the seven southern slave-owning states when someone who wasn't even on their ballot was pronounced the President of the USA. This is why they seceded from the union before Lincoln was even sworn into office saying, "He's not my president". The other three states seceded shortly after the first seven. Those 10 states made up the confederacy.