To have a cold is to be sick. If you have a cold, you may still feel okay, but you should take the precautions you would take if you had the flu. Even if you just have a wee cold, you shouldn't keep too close to people or share drinks/food. You should try and get more rest and drink lots of water.
Generally, a 'cold' is just sniffles and feeling a bit off or slow.
Being 'sick' would be minor headache, runny nose, lost appetite, tiredness, maybe sore joints.
Having the 'flu' or worse would be all of the above plus harsh vomiting, hot and cold spells, inability to focus, and just feeling terrible.
if you have a flu as opposed to a cold, you will have a high temperature and body aches usually.