Just as a side note, <button> will implicitly submit, which can cause problems if you want to use a button in a form without it submitting. Thus, another reason to use <input type="button"> (or <button type="button">)
Edit – more details
Without a type, button implicitly receives type of submit. It does not matter how many submit buttons or inputs there are in the form, any one of them which is explicitly or implicitly typed as submit, when clicked, will submit the form.
There are 3 supported types for a button
submit || "submits the form when clicked (default)"
reset || "resets the fields in the form when clicked"
button || "clickable, but without any event handler until one is assigned"