Differences
.append accepts Node objects and DOMStrings while .appendChild accepts only Node objects
const parent = document.createElement('div');
const child = document.createElement('p');
// Appending Node Objects
parent.append(child) // Works fine
parent.appendChild(child) // Works fine
// Appending DOMStrings
parent.append('Hello world') // Works fine
parent.appendChild('Hello world') // Throws error
.append does not have a return value while .appendChild returns the appended Node object

In cases where you can use .appendChild, you can use .append but not vice versa.