These terms refer to different properties of the employment arrangements and they're not explicitly contrastable.
- Full-time employment means you are working at least ~35 hours a week, i.e. a 'normal' working week in that job. The actual number of hours varies by country and might not have an exact value in law. It contrasts with part-time employment, which is where you work fewer hours for proportionately less pay, and the proportionate calculation of pay, holiday, and (sometimes) other benefits is known as a pro rata arrangement.
- Employment can also be either permanent or temporary. In the former case, the employer wishes to hire someone and has no specific end-date in mind. In a temporary contract (in some cases knows as a fixed-term contract), the employer already has an end date in mind, e.g. because the employee is providing maternity cover or helping out during a busy period which will not last. In the UK, most fixed-term contracts will say the employer can choose to end the contract early, so this confers no legal advantage to the employee - they can still be fired before the intended end date, but they can also be dismissed by the employer when the contract period ends slightly more easily than in the case of a permanent contract.
In all cases there is said to be an employment contract, although it may not be written down, it may be composed of verbal agreement and custom and practice.
Working as an independent contractor is something different again and may not be an employment relationship in law. In this case you may be effectively self-employed (NB: employment and tax arrangements vary by jurisdiction on this), and typically will have multiple clients over a period of time. The relationship is closer to a business-to-business relationship, and what you are paid will have to pay for not just your income but also your holiday, sickness cover, pension, and some taxes that the employer would otherwise pay.