All governments are the same

Federal government

The Federal Government is - alongside the Federal President - the highest body of the executive. The members of the Federal Government are: Federal Chancellor, Vice Chancellor; Federal Ministers and State Secretaries. They act as a joint body and the decisions of the federal government are unanimous, i.e. a proposal will only be implemented if everyone agrees. In order to coordinate the joint approach, the members of the Federal Government meet for the Council of Ministers (this meeting usually takes place once a week). The state secretaries are not entitled to vote in the Council of Ministers.
The most important person in the Federal Government is the Federal Chancellor; he / she is formally on an equal footing with other members of the government, but has the opportunity to name those persons who will then become ministers. This is called "primus inter pares" - that is, "first among equals".
If the federal government is formed by only one party, that is Sole government. To do this, one party must receive an absolute majority of seats in the National Council election (i.e. at least 92 out of 183). In Austria this was the case from 1966–1970 (ÖVP sole government) and from 1971–1983 (SPÖ sole government).
A party can also form the government on its own, although it does not have an absolute majority in the mandate - this is called Minority government. The ruling party then needs the support of one or more other parties for decisions in the National Council. This has only happened once in Austria: in 1970 the SPÖ won 81 of 165 mandates (183 mandates only existed since 1971), but was able to govern with the support of the FPÖ.
A Coalition government is formed by two or more parties. A big coalition (i.e. the two strongest parties form the government) existed from 1947-1966, 1987-2000 and 2007-2017. Until 1966, the ÖVP provided the Federal Chancellor, then the SPÖ. If two other parties together form the federal government, one speaks of one small coalition (e.g. 1983–1987 SPÖ and FPÖ; 2000–2007 and 2017–2019 ÖVP and FPÖ or BZÖ; since 2020 ÖVP and The Greens).
Finally there is one more Concentration government: The government is formed by all parties represented in parliament (in Austria from 1945–1947; at that time the ÖVP, SPÖ and KPÖ were represented in the National Council, all three formed the government).
The government is sworn in by the Federal President (swearing in).