A sign which is referred to as an אות is any prediction that may be ordinary in
nature such as predicting an earthquake or a storm, or a prediction that may be
miraculous in nature such as water turning to blood or a stick turning into a snake.
As long as this prediction is given peforehand, it can be considered a sign that what
one says is true.
Rashi in Parshas Ekev says that the reason that the stick was called a sign was
because Hashem gave it to Moshe as a sign that he was acting as Hashem’s messenger
and not acting on his own.
This is why it says that “signs” refers to the stick even though when the stick
actually changed to a snake, it was also considered a “wonder.”
Many of the makos were considered “signs” and certain components were even
miraculous in nature and therefore were also considered “wonders.” For example,
the mako of Hail was in part something that occurs in nature yet the mixture of fire
within the center of the hailstones was miraculous in nature. This is why many of the
makos are considered both “signs and wonders.”
While all the makos represented nature running wild and were in part miraculous
in nature, the only mako that was completely miraculous in nature was the mako דם
of – “Blood.” This is why the Haggadah says הדם זה ..ובמופתים