People have different interpretations of the word heimish. My husband’s family is heimish – and the way I’ve heard it defined most is that you come from chassidish background, and may have a few chassidish minhagim, but not chassidish all the way. My guess is that the connection to the word “heim – or home” is that they are following some of their traditions from the alte heim, but that’s my own take on it.
It is not the OPPOSITE of yeshivish – as you can be both – we are also yeshivish. And of course there are different interpretations of yeshivish, but that’s another whole topic lol.