This is more general PHP than anything WordPress specific.
String concatenation occurs whenever you combining two stings with the .
operator. During string concatenation some basic PHP keywords will not apply and you’ll need to use the shorthand equivalent instead. In this case you can use the ternary (conditional) operator
$html.= '<span class="cat">In '. ( $terms_string === "Articles" ) ? 'glyph HTML code' : '' .' <a href="'. $typeLink . '">' . $terms_string . '</a></span>';
A better, more readable format may be breaking up the HTML output into multiple strings:
$html.= '<span class="cat">In ';
if( "Articles" == $terms_string ) {
$html .= 'glyph HTML code';
}
$html .= '<a href="'. $typeLink . '">' . $terms_string . '</a></span>';