"if(true){a} else {b}" or just (a||b)

(are both equally correct?)

A statement block like if(true){a} else {b} does not evaluate to any value (but see Note 1 below), but an expression like (a||b) always does. Therefore, IMHO it's not correct to say these are equivalent or "equally correct." The if/else-statement block can be made to have an effect equivalent to the expression, but only if the a b expressions or statement(s) have the correct side effects.

An expression can always be incorporated into another expression — if precedence is handled properly! A statement cannot be incorporated into another statement unless you contort your program logic with some sort of usually unnecessary eval nonsense. E.g.:

Win8 Strawberry 5.8.9.5 (32)  Wed 10/28/2020 15:06:58
C:\@Work\Perl\monks
>perl -Mstrict -Mwarnings
my $x;  # undefined/false
my $y = 'default string';

my $side;
if (not $x) { $side = $y; }  # true clause has side effect
# $side = $y unless $x;  # a more terse alternative

printf "side effect '%s'  logical-or '%s'  ternary '%s' \n",
        $side,            ($x || $y),      $x ? $x : $y;
^Z
side effect 'default string'  logical-or 'default string'  ternary 'de
+fault string'
[download]

Notes:

1. An if- or if/else-statement block like
       if (CONDITION) { statements(s)  }
   or
       if (CONDITION) { statements(s)  } else { statements(s) }
   will return a value from a subroutine if it is the last thing executed in the subroutine, but this behavior is inherent to the behavior of subroutines, and not directly related to the behavior of conditional statement blocks.
   
   Update: To be more precise, what is returned from a subroutine that has no explicit return statement is the value of the last statement or expression executed in the subroutine. So in the subroutine

   sub func {
       ...
       ...
       if ($x) { foo(); bar(); } else { fee(); fie(); }
       }
   [download]

   the return value of bar() is returned by func() if $x is true, that of fie() if $x is false.

   Win8 Strawberry 5.8.9.5 (32)  Wed 10/28/2020 22:49:24
   C:\@Work\Perl\monks
   >perl -Mstrict -Mwarnings
   printf "'%s' returned from true clause \n",  func(1);
   printf "'%s' returned from false clause \n", func();
   
   sub func {
       my $x = shift;
       printf "x is %-7s", $x ? 'true' : 'false';
       if ($x) { foo(); bar(); } else { fee(); fie(); }
       }
   
   sub foo { return 'from ' . (caller 0)[3]; }
   sub bar { return 'from ' . (caller 0)[3]; }
   sub fee { return 'from ' . (caller 0)[3]; }
   sub fie { return 'from ' . (caller 0)[3]; }
   ^Z
   x is true   'from main::bar' returned from true clause
   x is false  'from main::fie' returned from false clause
   [download]