das Stadium
stage
A particular section or phase in a development, process, or disease.
Die Verhandlungen sind in ein kritisches Stadium getreten.
The negotiations have entered a critical stage.

stage / stadium
Loading your saved state.
stage
A particular section or phase in a development, process, or disease.
Die Verhandlungen sind in ein kritisches Stadium getreten.
The negotiations have entered a critical stage.

In the meaning 'phase', 'Stadium' (stage) is usually used with the preposition 'in' and the dative. Typical verbs are 'sein' (to be), 'sich befinden' (to be located/to be), 'eintreten' (to enter), or 'erreichen' (to reach).
Das Projekt befindet sich noch in einem frühen Stadium.
The project is still in an early stage.
'Stadium' (stage) is often combined with adjectives that describe a phase in a process, for example 'frühes Stadium' (early stage), 'fortgeschrittenes Stadium' (advanced stage), or 'letztes Stadium' (final stage).
Die Krankheit wurde zum Glück in einem sehr frühen Stadium entdeckt.
Fortunately, the disease was discovered at a very early stage.
This meaning of 'Stadium' (stage) is found in contexts that describe a process or development. These include projects, negotiations, diseases, or biological developments.
Die Raupe ist ein Stadium in der Entwicklung eines Schmetterlings.
The caterpillar is a stage in the development of a butterfly.
In the meaning of a sports facility, 'Stadium' (stadium) refers almost exclusively to historical or ancient structures. This word is not used for a modern sports arena.
Bei der Führung durch Rom besichtigten wir ein altes römisches Stadium.
During the tour through Rome, we visited an old Roman stadium.
status / stand
'der Stand' and 'das Stadium' can both describe how far something has developed. 'der Stand' means the current state or progress at a certain point in time. 'das Stadium' more often means a particular phase within a development, a process, or an illness. You can confuse the words when talking about progress. If you are asking 'How far along are we right now?', 'Stand' fits. If you want to name a phase, 'Stadium' fits.

Die Ärztin erklärt, in welchem Stadium die Krankheit ist.
The doctor explains what stage the illness is at.
Nach der Pause besprechen wir den Stand der Vorbereitung.
After the break, we discuss the status of the preparations.