Yes. „Vă rugăm” would mean that you and at least another person are asking someone to do something. „Vă rog” means that only you are asking. Literal translations should help you understand better:
Vă rog - I ask/am asking you (to do something) - formal (or informal when talking to more people)
Vă rugăm - We ask/are asking you - formal (or informal when talking to more people)
Te rog - I ask/am asking you - informal (just one person you are talking to)
Te rugăm - We ask/are asking you - informal (just one person you are talking to)
This actually works with every pronoun (except first person, obviously): o rog/o rugăm (asking her), îl rog/îl rugăm (asking him), îi rog/îi rugăm/le rog/le rugăm (asking them).
btw. what I also found out by now is that when I and also someone else want to say thanks together, we say mulțumim. Atunci mulțumim pentru răspunsul tău.
Hey, really quickly, how did you do the accented t and a? Even with the international keyboard where you use right alt, I couldn't find the way to do it. Thanks in advance!
On my keyboard, if i hold down on a certain letter, variables of that letter comes up on the screen. Slide your finger to the accented letter you want. Hope that works for you.
When I use my smartphone then I also switch to romanian keyboard and do as od3rTZl5 said. When I use my PC I use the romanian programmer's keyboard and Alt Gr + a for ă, Alt Gr + q for â, Alt Gr + t for ț.
It is a little bit different than it is in french then. Because the terminaison would change only according to the person you ask to do something. Not according to who is asking for something.