A direct thermal printer prints on heat-sensitive paper without a ribbon. It is cheap and simple, but the label fades with sunlight, heat and time, so it suits shipping labels, receipts and short-lived price tags.
A thermal transfer printer prints through an ink ribbon. The image is far more durable, and you can print on paper, synthetic and film materials. For long-shelf-life products, asset tracking and marking codes, thermal transfer is the usual choice, because the code must stay readable for the product's whole life.
Also consider print volume (desktop, industrial or mobile printer), resolution (dpi) and code size: small DataMatrix codes benefit from higher resolution. BDB helps choose the printer, ribbon and labels as one matched set.