Infinite loop vs infinite recursion. Are both undefined?

No there is no difference. [basic.progress]p1:

The implementation may assume that any thread will eventually do one of the following:

• terminate,

• make a call to a library I/O function,

• perform an access through a volatile glvalue, or

• perform a synchronization operation or an atomic operation.

It doesn't matter how you have your infinite loop; if it doesn't do any of the points above, you get UB. Including the following:

int bar(int cond) {
    if (cond == 42) bar(cond);
    return 42;
}
bar(some_user_input);

The compiler is allowed to assume that some_user_input will never be 42.