If you ignore the cease and desist their next step is to sue you in court where the lawyers fight it out. They can sue immediately, without a cease and desist at if they want. However the reason to do a cease and desist is it costs a lawyer just a few minutes to write one up, while court often costs millions of dollars - thus if you just stop doing something after the cheap letter it is typically best for them to ignore the what they could have got by taking you to court right away. They can bring a cease and desist to court and show that they gave you time to stop which looks good to the judge and can influence how much the judge awards if they win (if they lose the cease and desists is at best meaningless).
A default judgement is when they sue and nobody shows up in court. Because you don't defend yourself the courts just assume you are guilty (assuming the case isn't completely absurd). Sometimes you can get a default judgement when it is obvious someone is doing something bad but not who, and then if you later identify who you can collect immediately - but that person you accuse can fight the default judgement in a lot of ways.