Flu is an upper respiratory tract infection usually accompanied by a fever, caused by an influenza virus (one of myriads of strains). Influenza type A is usually severe, whereas C is milder (but you still have flu and would still test positive for it).
A 'cold' is an upper respiratory tract infection which may or may not be accompanied by a fever, usually caused by rhinoviruses.
Symptoms are similar. Flu A tends to be the severe, rapidly mutating type with multiple strains and subtypes (think bird flu / swine flu). Flu B mutates less rapidly, can be as severe as flu A but isn't generally as common. Flu C is a mild upper respiratory infection.
Rhinoviruses can affect anywhere - usually in the upper respiratory tract, lower tract infections are rarer but can occur. Symptoms are more of congestion, sneezing, sore throat, headache. They can also be associated with ear infections / ear pain (more so than flu).
Generally speaking, if you have flu A / B you will have the usual upper respiratory symptoms plus joint pains, lethargy, sustained fever, fatigue.
Generally speaking, if you have a cold you will have a cough/sore throat/snotty nose, may not have such a high fever and may have less fatigue.
However. Generally speaking isn't "every case of flu feels like death", "if you can post here you don't have flu" and there are cases of rhinovirus infection that can make you feel truly horrendous.
In practice it shouldn't make a difference unless you have other illnesses where flu may be dangerous (you can get a nasty staph pneumonia on top of flu if you have lung issues or immunosuppression). Keep hydrated, keep warm / cool as temperature directs, take simple anaglesia and anti-inflammatories for symptom control if you need them and seek medical help if you become so unwell you can't cope at home, have difficulty breathing or chest pain, start coughing up blood or any other symptom that worries you.
And stay off work until you're better, everyone else doesn't need it ;)