What is the difference between all real numbers and no solution how do you know when these situations occur

For a solution of 'all real numbers' to occur, you must end up with a statement that is true no matter what

example

simplifying results in x=x or 8=8 or 0=0 or something liek that

an example equation would be 2 (x+1) = 2x+2, simplifies to x=x or 2=2 or 0=0

no solution is when you get a false statement from simplifying

example, 3=4 or - 1=0

an example equation could be 2 (x+1) = 2x+3, it simplifies to 2=3 which is false