Full-time is the word opposite to part-time, means that you are working 9-6pm every weekday or not.
contract / temp / permanent, means how long your term of employment is with this company. For instance, i am on 2-yr contract now, but i am definitely not a temp, nor a permanent. my boss is also on 2-yr contract and our board of directors only agree to inject money for a few years, that's why we are on short-term contract. permanent means there is no limit, but u can still be fired the next day if your company is willing to pay the money in lieu. that happened to my ex-colleagues. temp is really temp.
usually, as long as it's permanent or contract for a full-time job, the company has to abide certain rules and regulations by MoM of Singapore. but the sg law is very pro-company and not really protecting the employees. u may check it out and be careful when u r signing any contract. do consider it for at least one day, and check any necessary documents, government website, to fight for your own rights.