In a second marraige, the bride follows the usual process to become tehora before her wedding: she performs a hefsek taharah, observes the seven clean days, and immerses in a mikveh before the wedding, up to four days beforehand. As you wrote, there is no requirement to separate after the first act of relations, and therefore she may want to try to time her wedding so that the couple have more time together before she becomes niddah again.

In addition, the ketubah will not read "betulah." Also, if it is a second wedding for both the bride and groom, sheva brachot will be recited on the day of the wedding, but not during the week that follows.

These are the main halachic differences. There may be some differences in wedding customs, depending on the community; this should be discussed with the officiating rabbi.