Sticking to your approach, just grab the string index for $start, use that as offset to $stop, and look for "\n" (note that '\n' is not the same thing)
$start='Richland';
$stop="\n";
$startI = strpos($s, $start);
$stopI = strpos($s, $stop, $startI);
$text=substr($s, $startI, $stopI - $startI);
I'd also start checking for $stopI > $startI. If you search for a nonexistent $stop, $stopI will be false, and $stopI - $startI => 0 - $startI => get text from $startI up until $startI characters from the end.
$start='Richland';
$stop="Does not exist";
$startI = strpos($s, $start);
$stopI = strpos($s, $stop, $startI);
if ($stopI > $startI)
$text=substr($s, $startI, $stopI - $startI);
else
$text = '';