There's a big difference between the two of them . Flu will pretty much land you in bed (and if it doesn't, it's not flu, it's just a bad cold and even then some colds are pretty horrible).
And if you do genuinely have the flu and think you can carry on (I know one girl who came into uni once for a test and she had been diagnosed with the flu, she looked really awful) you're not doing yourself or anyone else a favour. You're just spreading your germs around, possibly to people who are less able to handle it and more prone to complications of the flu than you are, and prolonging your own recovery. You're better off staying in bed, getting plenty of rest, making sure you get enough fluids and taking OTC meds for aches etc.
Which is all you can do for colds as well, treat the symptoms-stock up on tissues, drink lots of hot drinks or get some lozenges if you've got sore throat, take paracetamol or ibuprofen for aches and pains.
I get the flu vaccine every year because I have asthma, and luckily I'm yet to have ever had the flu. I've had some horrific colds where I've had to take a day or two off uni, but I don't do anything other than the above-drink lots of hot drinks, make sure I've got tissues, take paracetamol if I've got a headache or other aches and keep my inhaler close by (as they make me wheezy and go straight to my chest every time). I wouldn't take a day off work for a cold, but I do make sure I wash my hands frequently if I do have one and am in work because I don't want to spread it around anyone else.