Maybe it helps to understand the general architecture of how programs are parsed.
In a nutshell, there are two stages to parsing a program (C++ or others): lexer and parser.
The lexer takes the text input and maps it to a sequence of symbols. This is when spaces are handled because they tell where the symbols are. Spaces really matter at some places (like between int and c, to not confuse with the symbol intc) but not others (like between a and ++ because there is no ambiguity to separate them).
The first example:
int c = a++ +b;
gives the following symbols, each on its own row (implementations may do this in slightly different ways of course):
int
c
=
a
++
+
b
;
While in the other case:
int c = a+ ++b;
the symbols are instead:
int
c
=
a
+
++
b
;
The parser then builds a tree (Abstract Syntax Tree, AST) out of the symbols and according to some grammar. In particular, according to the C++ grammar, + as an addition has a lower precedence than the unary ++ operator (regardless of postfix or prefix). This means that the first example is semantically the same as (a++) + b while the second is like a+ (++b).
For your examples, the ASTs will be different, because the spaces already lead to a different output at the lexer phase.
Note that spaces are not required between ++ and +, so a+++b would theoretically be fine, but this is not recommended for readability. So, some spaces are important for technical reasons while others are important for us users to read the code.