A Yo'etzet Halakhah is there to answer questions that are going unasked because some women are understandably embarrassed to raise them with a male rabbi. They can also find answers that wouldn't cross a man's mind simply because the territory is more familiar. The only halachic decisions they give are ones where the questioner's community has a well established consensus ruling. If a decision requires discretion, ie "pesaq" or "hora'ah", they will consult with a poseiq, a rabbi.
(For all of the above, see http://www.yoatzot.org/questions-and-answers/answer.asp?id=1157 , from the the website of Nishmat, Rebbetzin Chana Henkin's seminary for producing yo'atzot.)
According to Rav Uzziel, the term "yo'etzet" comes from the Amidah. "Hashiva shofeteinu kevarishonah, veyo'atzeinu kevatchilah -- restore our judges like at first, and our advisors like in the beginning." The rabbinate continues the work of the shofeit, these women continue the work of the yo'etz. And is decidedly not that of rabbi.
A Maharat's diploma is considered ordination and calls itself by the same term -- semichah http://www.jta.org/2013/06/17/default/what-does-an-orthodox-ordination-certificate-look-like . While it doesn't say "Toreh Toreh" the female conjugation of "Yoreh Yoreh" (Can he decide halakhah? He can decide!) found on a standard rabbinic ordination, it does say "heter hora'ah lerabbim -- permission to give rulings to the masses." It is "rabbi" in all but name and in fact some are calling themselves "rabbah", such as the dean of Yeshivat Maharat -- Rabba Sara Hurwitz http://www.yeshivatmaharat.org/faculty-and-staff/2014/5/21/rabba-sara-hurwitz-dean
This is why there is broader acceptance of Yo'atzot than Maharatot: The motivation for creating Yo'atzot is to increase observance of Taharas haMishpachah. Traditional gender roles are preserved, and practical interpretation of halakhah is kept in the hands of people capable of qualifying to become judges. The Maharat is an acknowledgement of feminist ideals, the dignity and authority of today's woman, the level of Jewish education available to them, and consequently a belief that the rabbinate should be open to women.