${...} is a syntax for another purpose. It is used to indirectly reference variable names. Without string interpolation, literal names in curly braces or brackets are written as string literals, thus enclosed in quotes. However, inside interpolation quotes are not used outside curly braces:
$bar = 'baz';
echo $bar , PHP_EOL;
echo ${'bar'} , PHP_EOL;
$arr = ['a' => 1, 'b' => ['x' => 'The X marks the point.']];
echo $arr['a'] , PHP_EOL;
// interpolation:
echo "$arr[a] / {$arr['a']}" , PHP_EOL;
Instead of literals you can use functions as well:
function foo(){return "bar";}
// Here we use the function return value as variable name.
// We need braces since without them the variable `$foo` would be expected
// to contain a callable
echo ${foo()} , PHP_EOL;
When interpolating, you need to enclose into curly braces only when the expression otherwise would be ambiguous:
echo "$arr[b][x]", PHP_EOL; // "Array[x]"
echo "{$arr['b']['x']}", PHP_EOL; // "The X marks the point."
Now we understand that ${...} is a simple interpolation "without braces" similar to "$arr[a]" since the curly braces are just for indirect varable name referencing. We can enclose this into curly braces nevertheless.
Interpolated function call forming the variable name:
echo "${foo()} / {${foo()}}", PHP_EOL;
// "baz / baz" since foo() returns 'bar' and $bar contains 'baz'.
Again, "${bar}" is equivalent to ${'bar'}, in curly braces: "{${'bar'}}".
As asked in comments,
there is another curly brace syntax to reference array keys.
$someIdentifier{'key'}
This is just an alternative syntax to PHP's common array syntax $array['key'].
In opposit to the latter, on indirect variable name references the curly braces follow immediately after the $ or the object member operator ->. To make it even more cryptic we can combine both:
$bar['baz'] = 'array item';
echo ${'ba' . 'r'}{'ba'.'z'};
which is equivalent to echo $bar['baz'];
Really weird in PHP's string interpolation: "${bar}" is valid and "${'bar'}" as well but not "$array['key']", "$array[key]" is valid instead, but both, "$array{key}" and "$array{'key'}", do not work at all.
Conclusion
It should be made a habit to use braced interpolation syntax all the time. Braced array key syntax should be avoided at all.
Always use:
"{$varname} {$array['key']} {${funcname().'_array'}['key']}"
See also PHP documentation:
(to distinguish from)