How to output wordpress custom tags separated by comma?

Question

You have a couple of flaws here:

ALWAYS code in a way with a mindset of that your code will fail. This is very important. Most people code with a perfect world mindset. A perfect world will never happen. Always think of what will happen when your code fail.

As example, in your code, $terms return an object of term objects if everything pans out. $terms also returns an empty array if there are no terms in the taxonomy or terms without having any posts. It also returns a WP_Error object if the taxonomy does not exist. This is all bugs. Invalid taxonomy you may ask. If you have correctly registered your taxonomy in a plugin, and you disable that plugin, your taxonomy does not exist anymore, which will trigger the invalid taxonomy error.
You should start your counter outside your foreach loop. Not inside
The get_ prefix is used for functions that returns its output, not echo it.
Always sanitize and validate

I will rewrite your code to look something like this: (NOTE: Requires PHP5.4 +)

function get_taxonomy_food_tags( $taxonomy = '', $args = [] )
{
    // Check if we have a taxonomy and that it is valid. If not, return false
    if ( !$taxonomy )
        return false;

    // Sanitize the taxonomy input
    $taxonomy = filter_var( $taxonomy, FILTER_SANITIZE_STRING );

    if ( !taxonomy_exists( $taxonomy ) )
        return false;

    // If we reached this point, our taxonomy is valid. So lets continue. Get our terms
    $terms = get_terms( $taxonomy, $args );

    // We will only check if we have terms, we know our taxonomy is valid because we have reached this point
    if ( empty( $terms ) )
        return false;

    // Great, if we got to this point, we have terms, lets continue
    // Define our variable to hold our term links
    $term_links_array = [];
    foreach ( $terms as $term ) {
        $term_link = get_term_link( $term );

        // Make sure we do not have a WP_Error object, not really necessary, but better be safe
        if ( is_wp_error( $term ) )
            continue;

        // Build an array of term links. Let php do the hard work and calculations
        $term_links_array[] = '<a href="' . esc_url($term_link) . '">' . $term->name . '</a>';
    } // endforeach

    // Make sure that we have an array of term links, if not, return false
    if ( !$term_links_array )
        return false;

    // We have reached this point, lets output our term links
    return implode( ', ', $term_links_array );
}

You can now use it as follow

echo get_taxonomy_food_tags( 'food_tag' );

I have also introduced a second parameter which you can use to pass an array of arguments to the internal get_terms() function, so you can use the new function in the same exact way as the default get_terms() function

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