According to Wikipedia:

The term “webinar” is a portmanteau of web and seminar, meaning a presentation, lecture, or workshop that is transmitted over the web.

The term “webcast” derives from its original similarity to a radio or television broadcast. Early usage referred purely to transmission and consumption of streaming audio and video via the World Wide Web. Over time, webcast software vendors have added many of the same functional capabilities found in webinar software, blurring the distinction between the two terms. Webcasts are now likely to allow audience response to polls, text communication with presenters or other audience members, and other two-way communications that complement the consumption of the streamed audio/video content.