Sorry for the confusion. Part of the problem with providing a truly concrete answer, is that there is no single source of truth. Each field of study calls the same analysis by different names, have analyses unique to that field, etc. There is no authoritative body that defines anything. Therefore, you get discussions like this. If you do a little online research focusing solely on universities, you will still get contradictory answers.
The graphs below show a histogram of continuous and discrete data. Both have the same x-axis scale and are binned the same. Note that the discrete Poisson data only occur at integer values while the continuous normal data occur at decimal values also.