I remember learning something about the process of marriage having several steps (for example: bedeken, erusin, chuppah, yichud) with the final step being consummation. If this is the case, does it follow that if the marriage remains uncosummated, it is "incomplete" in some way? If so, what are the halachic implications of this status?
נכנסה לחופה ולא נבעלה is mentioned many times in the Gemarah, and there are numerous differences. Kesubos 56A discusses if she gets the additional monies written in the Kesuba is such a case. The Gemara in Nidah 19B also discusses a different halacha in this case.
Practically, the Bach and Bais Shmuel in Even Haezer 64:2 understand the language used by the Shulchan Aruch (and Rambam) that only a "Beula" has 3 days of Simcha, to mean that a case of נכנסה לחופה ולא נבעלה would indeed have a full 7 days of simcha if she got divorced or the husband died and she remarried. The Shulchan Aruch states;
הנושא את הבעולה צריך לשמוח עמה ג' ימים בין בחור בין אלמון וי"א דבחור שנשא בעולה צריך לשמוח עמה ז' ימים (והאשה יכולה למחול על שמחתה) (ר"י נכ"ב):
One who marries a previously married woman is required to celebrate with her for three days, whether he was previously married or not. There are some who say that a man who was never married previously who marries a previously married woman needs to celebrate with her for seven days. (Rema: And the woman needs forgiveness for her joy, Rabeinu Yeruchum, 22).
To which the Bais Shmuel adds;
מדייק ב"ח אם היא אלמנה ואין בעולה צריך לשמוח עמה ז' ימים
I am sure there are many other differences as well