Parshas Vayikra describes the different types of oaths - shevuas bitui - an oath of utterance, and shevuas haeidus - an oath of testimony. A shevuas bitui can refer to the past or the future. Whereas a shevuas bitui l'habah (an oath of utterance referring to the future) obligates an individual to engage in or refrain from a given activity, a shevuas bitui l'sehavar affirms or denies what has already occurred. A shevuas haeidus allows a litigant to insist that an individual either testify or assert through an oath that he is unaware of any relevant testimony. Should that individual swear falsely, he must offer a Korban Oleh V'yored.
Unlike a shevuas bitui which an individual initiates himself, a shevuas haeidus can be imposed by others. A litigant can approach a potential witness and adjure him to affirm his denial of testimony (mushba mipi acheirim). This might stem from the Torah's insistence that a witness testify - im lo yagid v'nasa avono.
The Netziv (Breishis 24:3, see Harchev Davar) explains that the right to impose a shavua can be broadened beyond the example of shevuas haeidus. When Avraham Avinu instructs his servant Eliezer to find a suitable wife for Yitzchok, the term "v'ashbiacha" is used, implying that Avraham Avinu imposed a shavuah. The Netziv explains that because a servant must obey his master, an oath can be imposed. Similarly Shlomo Hamelech confronted Shimmy stating (Melachim I:2:44) "halo hishbaticha b'Hashem" indicating that a king can impose an oath on his subjects. Furthermore, the Netziv suggests that the Sanhedrin has the right to impose a shavuah. Accordingly the Sanhedrin would impose an oath, mushba mipi acheirim, on the kohein gadol prior to Yom Kippur to ensure that the avodah would be performed properly. All of these examples are rooted in the model of shevuas haeidus, where the concept of mushba mipi acheirim originates.
At times, one who takes an oath must invoke Hashem's name. Rabbeinu Tam maintains (Ran Nedarim 2a) that this is only necessary in cases where an oath is imposed - mushba mipi acheirim. We mention Hashem's name as if to state: by virtue of the authority granted by the Torah I hereby impose this oath. The Netziv observes that in each of the above cases the name of Hashem is used in the passuk, supporting the distinction of Rabbeinu Tam.