No not quite, the F1 is best regarded as a hybrid of two parent plants which have
some of the characteristics that you want in your plant, but when they are crossed with each other produces the plant that you want.
But if you then pollinate two of your F1 plants together the resulting off spring will be different again. These are known as F2's
But if you say, buy a pack of Scarlet Emperor runner beans they are not F1, but bred from trusted stock that breeds true.
So then if you pollinate two of these plants together their offspring will still be true to the "scarlet emperor" attributes.