Allah's description of that Day ['Day of the Covenant'] didn't stop there. It went onto the next verse in which it is demonstrated that the people who testified to Allah (ﷻ) being their Lord acknowledged/understood Tawheed (Oneness of God) to the point that they could not use their ancestors' shirk as an excuse to hide behind.
7:172: And [mention] when your Lord took from the children of Adam - from their loins - their descendants and made them testify of themselves, [saying to them], "Am I not your Lord?" They said, "Yes, we have testified." [This] - lest you should say on the day of Resurrection, "Indeed, we were of this unaware."
7:173: Or [lest] you say, "It was only that our fathers associated [others in worship] with Allah before, and we were but descendants after them. Then would You destroy us for what the falsifiers have done?"
Further explanation from Islamweb:
This verse indicates that Allah inspired all of mankind with the fact that He is their Lord and that they have no other lord or deity but Him. This is the covenant that Allah took from mankind: {They said, "Yes, we have testified."} Therefore, it is no longer acceptable that they say on the Day of Judgment that they forgot and were unaware of the covenant or claim that their fathers associated other partners with Allah and they thus followed them because they are their descendants. The polytheism of one's fathers is not an excuse for the offspring to deviate from the covenant of the fitrah (natural disposition) because it is a covenant between them and Allah, and their fathers have nothing to do with it.
Conclusion:
Although it may not linguistically be necessarily the same.. the Qur'an verse establishes that the people who took that testimony (i.e., all of us) understood "you [Allah] are our lord" and "there is no deity worthy of worship but Allah."
