Flu is a very serious illness caused by the influenza virus, it is very unpleasant, and can cause death. People suffering from flu should stay in bed, so they don't die, and so they don't infect others. The cold is much less serious, and is caused by a completely different virus. Some of the symptoms can be similar - fever headache, cough etc., but flu is much, much worse. Many people also suffer from hypochondria, a psychological condition which makes them believe they are ill when they are not. This is very common: when a hypochondriac has a bad cold, they will often describe it as flu. Men are more known for doing this than women, which is why we sometimes call their condition 'man-flu'.

They are completely different, although people do get them mixed up. Influenza or flu is not just a very bad cold. It comes on very suddenly, and can be serious, sometimes even fatal. The flu virus evolves and changes from year to year, and can be much worse some years than others. Influenza vaccines ("flu shots") prevent flu, but because the flu strains are different every year you need to get the shots every year. The last time someone in my family caught the flu, they ran a fever of 39.5°C and the doctor told us that if ibuprofen and drinking liquids didn't bring it down within an hour, we should take them to the emergency room. (Fortunately the fever did come down). Colds are just a nuisance. They are caused by many different viruses and there is no immunization or cure. The chief symptoms of colds are coughing, sneezing, sniffling, and mild fever. Colds tend to begin slowly, sometimes with a tickle or scratchy feeling in the throat. Flu symptoms sometimes include diarrhea, nausea, and vomiting. Gastroenteritis can be caused by a virus; it's not really flu, but it is sometimes called "stomach flu." In the United States, the phrase "flu-like symptoms" is sometimes used as a euphemism for diarrhea, nausea, and vomiting.

You wouldn't really say "serious cold". It sounds a bit odd. You can say "I have a bad cold" although some people with these symptoms might say they have the flu as interchangeable with a bad cold although flu is includes fever etc.

We can say 'I have a bad cold', but the main difference between a cold and the flu is a high fever and the chills. Here is more information: https://www.healthline.com/health/cold-flu/cold-or-flu Hope this helps