Lots of things are well defined only to completely fail when it comes to being used in a real context. There are many obvious examples and even more less obvious examples.
Trump is a good example of a person who has said some racist things but even more things that were interpreted as racist.
We are all racist even if we don't want to be, we cannot help ourselves the question then becomes how do we let that affect us and how we act on that.
And so if it only takes one example to show someone is racist then we all are.
It's much less well defined once you look at the entirety and doesn't just take a sentence out of its context.
Language is tricky and defining something well does not mean it's easy to put things into these boxes.
You are right there is a difference and to the extent, it easy to identify this racist/sexist rhetorics we should obviously object to it.
But it's not much different when liberals paint all Trump voters racist. Very often do we see comments that were not meant racist suddenly be attacked simply because of the person who said it.
You are not a better person just because you are against racism if you base your judgment of what constitutes a racist or a racist remark on who said it and we shouldn't listen to you more by your own definition.
You can very easily be a Trump voter and not a racist and you can eve be a Trump voter and against racism or misogyny as that exist on both sides. Yet listening to the public debate one should think it only happens on one side.
Two wrongs don't make a right and yet it seems like most liberals (and I count myself amongst the liberal crowd) basically justify the sentiment you seem to be supporting with something along the lines of "well he/she started".
There are (luckily) very few racist in the Hitler sense of racist.