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The contractual reform in the UN system cut back on many different contract types. But the UN still knows different contract types and the distinction between staff contracts and non-staff contracts still exists.
The most common "regular" staff contract are the Fixed Term Appointments (FTA). These are the jobs that you will find in a lot of places in the system. The duration of Fixed Term Appointment (FTA) contracts is usually a year or two. Even though FTAs do not carry any expectation for renewal there is no limit and/or break in service in case the organization decides to extent an FTA.
Temporary staff contracts for up to a year minus one day of duration are Temporary Appointment contracts. This contract type may be closest to what used to be "Assignment for limited durations (ALD)" or "Temporary Fixed Term (TFT)" but is strictly limited in terms of duration (both ALDs and TFTs don't exist any longer). Temporary Appointments carry a "break in service" blackout period to prevent a series of TA contracts.
In the non-staff or consultant category things get complicated. First of all there is a very wide variety of contracts available. These contracts are typically called "Consultant Contract", "Special Service Agreement (SSA)", "Individual Contractor (IC)" or "Individual Contractor Agreement (ICA)". The conditions for these contracts can be quite different from organization to organization. Also more and more organizations see these non-staff contracts not as HR contracts but administer these under the organizations procurement rules. Typically these contracts carry very few employee benefits. Consultant contracts are either time-bound or per deliverable and often short-term. Many organizations do have break in service rules to prevent continuous employment on non-staff contracts but all of the non-staff contracts carry benefits since allow for more flexibility than staff contracts.
Within all these contracts different job grades (sometimes also called levels) exist. The International Civil Service Commission defined grades from ICS-1 to ICS-14 (let's end at ICS-14 for simplicity reasons). And within these levels there are two big categories. The first is the General Services category up to ICS-7 and then the Professional category usually starting at ICS-8. General Services Jobs often times don't require a Master's degree whereas jobs in the Professional grades often require a Master's degree (UPDATE: Also see comment below). General Service jobs are national jobs which means that these jobs are usually reserved for nationals of the country the jobs are located in. Professional category jobs can be international and national. National jobs are often times called "National Officer" (NO). If you are on a national contract you can expect to stay in the country and you will not be required to move. If you are on an international contract you can be re-assigned to any other place in this world, a fact that is sometimes forgotten about and that can lead to conflict if an organization actually tries to re-assign internationals.