I don’t know why “people” have any impressions that they have. You’d have to ask them. I’ve not encountered this as a broad-based phenomenon, whether among Catholics or non-Catholics. More often, people perceive that the Church has rules against abortion and contraception, or a ban on them, with no real clue as to what lay behind the “rules.” Most people don’t seem to think about it more deeply than that or more positively than that; the real answer is that both are wrong because they are contrary to the dignity of the human person.
I’m not sure the Church ever taught that they were the same, because that would be silly. They are clearly not the same. They are clearly born of the same mentality which is contrary to God’s design for human procreation, but they are not the same action, and I don’t know why it would have ever been taught that way.
Can you point to anyone saying that the Church has taught that abortion and contraception are the same thing? Otherwise, what you’re doing is to set up a strawman yourself.