while burning a movie using burn dvd on mac I am constantly getting errors

Have you tried cleaning the DVD drive? Lightly blowing air through the drive can get a lot of dust out - if any has collected.

But mainly, it's the lens that gets dirty and can only be easily cleaned with a disk designed to brush dirt off of the lens. Here's a page of them as an example. They all work the same way. There are one or two brushes glued to the data side of the disk. As the disk rotates, it brushes dirt off of the lens. And by "easily cleaned", I mean you don't need to take the drive apart to manually clean the lens.

No, you don't need an Apple drive. The mechanics in them is the same as any other DVD drive. I have had multiple DVD and Blu-ray drives over the years. Not one has ever been made by Apple.

When I got my M2 Pro mini, it had trouble burning disks on my external Blu-ray drive. This same drive had no problems with a 2018 mini. What the M2 didn't like was the USB hub I had the Blu-ray drive connected to, even though the 2018 mini worked fine with the same setup. Once I connected the Blu-ray drive directly to a port on the M2 mini, the problem went away.

Lastly, have you tried a new cable? If it's a standard USB-A connecter, look at the end of the cable. If it's white plastic, then it's - at best - a USB 2 cable. But most likely USB 1. If that's the case, try a USB 3 cable. Those will have blue plastic on the connector.

Exactly what model and sub-model of Mac are you using? Older Macs have built-in optical drives and did not need an external. Ports have changed in the 40 years since the first Macintosh. Details get you faster and more precise answers here.

Your equipment line indicate you are running a very old macOS version that may be contributing to the issues. Doing "About this Mac..." will not only show your model and sub-model but your current macOS as well. Example:

That can be caused by various issues:

1. Inexpensive disks.
2. Dirt in the drive.
3. Bad cable.
4. Connection is too slow.
5. The drive is faulty.