Is there a difference between lat pull-downs and regular pull-ups? Specifically the wide grip overhand version of both these exercises.
The biggest difference is your ability to increase or decrease workload (or amount you're moving). Pull downs can allow the person to pull as little as 10 pounds (right right there are variances in actual weight versus stated weight depending on the machine) while pull-ups are limited to a minimum of user body weight.
There are machines that offset user weight for pull-ups that could even out this discrepancy.
The other is availability. Anywhere there is a ledge/bar/etc over head, you can do pull-ups. Lat pull-downs are limited to machine access or potential stretchy band (we call them thera-band) with fixated overhead point access.
The other factor that stands out for me as a big difference is the use of stabilizer muscles when performing pull-ups. Unless you are trying to kip-up for cross-fit-like pull-ups, or muscle-ups... you have to have good form and a tight core to keep from swinging back and forth.
In terms of muscle building they are equal in speed, as for potential and functionality then the pull up wins.
Pull ups teach your body how to use as much muscles as possible. Things such as clenching your jaws, pointing the feet or tensing the glutes and abdomen can suddenly make the exercise more stable and allow for more repetitions or more weight.
Machines can't have the same effect due to their nature of stabilizing the rest of your body while isolating certain muscles, machines also have a limited amount of weight.