Originally, yes. However, ...
Different languages adopted different strategies to indicate formality. In German, one replaces "du" with "Sie" ("they"), which is third person plural. In Spanish, "tu" is replaced with "usted", from "vuestra merced", or "your (pl) grace".
English adopted the same pattern as French, where "thou" became the familiar form, and "you" the formal form. This was the usage in Shakespeare's time, which is evidenced in his plays. You can see characters call someone "you" until they are angry, and then call them "thou" as an insult. One line is even "I thou thee!" (or, "I call you 'thou'!"). (Sorry, but I forget which play.)