The difference lies in the structure, themes, and context of transmission. Traditional coplas have fairly clear rules: specific consonant rhymes, defined meter (generally octosyllables or décimas), and they deal with subjects ranging from love to satire or mockery, but always rooted in orality and communal experience. They were passed down from generation to generation, sometimes without written records, and people adapted them depending on the region. The ones you see on social media now tend to be more formally free, they mix formats, play with current language, and the meter isn't always so strict. Plus, many times they're more focused on quick humor or trending topics than on traditional narrative.
Now, I don't think it's exactly "deforming" the tradition. It's more of a natural evolution. It always happened that people took coplas and adapted them to their time; your grandmother probably also sang versions that her grandmothers modified. What's different is that back then circulation was slow and local, and now it's instantaneous and global. Social media versions carry less folkloric weight because they lack communal roots and generally don't last long, but if people keep singing and sharing them, they could eventually become something like tradition. The point is that both forms are valid in their contexts: your grandmother's coplas are living heritage, and Instagram's are more contemporary cultural expression with roots in that same thing.