Mod vs remainder?

I was solving this question - Problem - B - Codeforces
The idea was to calculate 3^(3n) - 7^n mod M.

*here % is used in terms of C++

  1. Now what I understand from c - What's the difference between “mod” and “remainder”? - Stack Overflow, is that -10%3 is -1 while -10 mod 3 is 2. mod and %(the remainder in C/C++) is same for positive numbers. Is this correct?

  2. When a question asks us to give the answer modulo 10e9 + 7, as in the above-mentioned question, is it asking about remainder or modulo? - as this Submission #120181564 - Codeforces submission failed while this Submission #120182114 - Codeforces passed. I used the idea from Modulo of Negative Numbers ( I believe this is applicable to modulo and not remainder so “modulo 10e9 +7” is talking about “mod” - which is obvious but I am so confused). If Yes, then can someone explained the “modulo twice” method in the above link?

Thanks in Advance for all the help.