Rambam (Hil. Nedarim 3:7) draws exactly this distinction, based on Nedarim 16b. He says:
ומפני מה נדרים חלים על דברי מצוה. ושבועות אין חלות על דברי מצוה. שהנשבע אוסר עצמו על דבר שנשבע עליו. והנודר אוסר הדבר הנדור על עצמו
Translation from Chabad.org:
Why do vows take effect with regard to mitzvot and oaths do not take effect with regard to mitzvot? Because when a person takes an oath he forbids himself from [partaking of] the entity mentioned in the oath. When, by contrast, one takes a vow, he causes the entity mentioned in the vow to be forbidden to him.
The footnotes there say that this is precisely a gavra vs. cheftza distinction.
In that same chapter, Rambam gives other practical differences between them. For example, matpis (saying "Y is like X") works only for nedarim, because you've declared X to be forbidden and therefore can make Y exactly like it, while that doesn't work for shevuos.
Saying that "I will do something" which is permissible - as in your example of "I will go to work" - is indeed a shevuah. A neder, by definition, is either declaring something to be forbidden to oneself, or taking on an obligation to bring a korban or give tzedakah (Rambam, ibid. 1:1-2 and Matnos Aniyim 8:1).