What is the difference between first-touch and last-touch attribution on a website?

Very likely. First touch credits the source that first brought a visitor to your site. Last touch credits the most recent tagged source before the conversion. A visitor who finds you through a social ad and buys a week later from a search click counts for social under first touch and for search under last touch. Neither is right in every case. First touch shows where demand starts, which suits awareness and prospecting budgets. Last touch shows what converted it, which suits retargeting and closing campaigns. The useful move is to store both and choose the lens at report time, rather than fixing one model forever. Linkrunner's Web SDK (beta) keeps both, and its web campaigns reporting API takes attribution=last_touch (the default) or attribution=first_touch.