Your code is wrong
Code:
{if $extra_fields[field].field_value and ($extra_fields[field].service_name eq "SERVICE_NAME15")}
<a target="_blank" href="{$extra_fields[field].field_value}">
{/if}
{if $extra_fields[field].field_value and ($extra_fields[field].service_name eq "SERVICE_NAME13")}
{$extra_fields[field].field_value} Planting Directions</a>
{/if}
You will not get what you need like this because "field" and "service name" are the same for both ifs in each loop.
What do you have in first field and what in the second? Can you give example?