Correct. As others have said if he doesn’t win the Republican ticket, which he most likely will not, he will run as an independant where he is also all but guaranteed to lose as well.
A primary election is held by the political parties to select their nominees for the offices to be elected at the upcoming general election. In a primary, Republicans run against Republicans and Democrats run against other Democrats. And, of course, if other parties qualify to appear on the primary ballot, their candidates run against each other as well. In a primary, you may vote on only one party’s candidates. You cannot split your ballot between the various political parties. A primary election may also be held for nonpartisan races in order to narrow the number of candidates for the general election.
A general election is between party nominees and any candidates without political party affiliation. The general election determines which candidates will occupy the office that is up for election. Statewide ballot proposals also appear on the general election ballot.
Regardless of your political affiliation it’s good to see people interested in and participating in the political process.