die Klasse
class
A group of students who are taught together at a school; a grade level.
Die Klasse 8b macht nächste Woche einen Ausflug.
Class 8b is going on a trip next week.

class
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class
A group of students who are taught together at a school; a grade level.
Die Klasse 8b macht nächste Woche einen Ausflug.
Class 8b is going on a trip next week.

The word 'Klasse' (class) is the basis for other words such as 'klassisch' (classical/classic) or the verb 'klassifizieren' (to classify). All these words share the basic idea of dividing things into groups or categories.
Die Biologen klassifizieren die neue Art.
The biologists are classifying the new species.
As an expression of enthusiasm, 'Klasse!' (Great!) is used like an adjective or an interjection and is not declined. You can use it as a standalone exclamation or in a sentence.
Du hast die Prüfung bestanden? Klasse!
You passed the exam? Great!
In a school context, 'Klasse' can mean the group of students or the classroom. Verbs of movement such as 'gehen' (to go) or 'kommen' (to come) usually point to the room ('in die Klasse gehen' = to go into the classroom). 'In der Klasse sein' can mean both.
Die Schüler gehen nach der Pause zurück in die Klasse.
The students go back to the classroom after the break.
In the school context, the prepositions and case are important. 'In der Klasse sein' (to be in the class; dative) describes membership or location. 'In die nächste Klasse kommen' (to move on to the next grade; accusative) describes promotion at the end of the school year.
Meine Tochter ist jetzt in der dritten Klasse.
My daughter is now in third grade.
To express high quality, 'Klasse' is often used in fixed expressions or compounds. Examples are 'Spitzenklasse' (top class), 'Extraklasse' (extra class/outstanding quality), or the expression 'eine Klasse für sich sein' (to be in a class of one's own).
Dieses Hotel ist eine Klasse für sich.
This hotel is in a class of its own.
In the meaning 'soziale Schicht' (social class), the word is mainly used in sociological, historical, or political texts. It is often part of compounds such as 'Arbeiterklasse' (working class) or 'Mittelklasse' (middle class).
Die Gesellschaft war in verschiedene Klassen unterteilt.
Society was divided into different classes.
status / stand
'der Stand' and 'die Klasse' can both say something about the position of people or things. 'der Stand' more often means a person's social or professional status, that is, what place someone has in a society or group. 'die Klasse' more often means a group or category, for example a social class or a quality level. Learners may confuse the words because both have to do with classification. As a practical rule, you can say: for an individual person, 'Stand' often fits; for a group or level, 'Klasse' is usually more appropriate.

In diesem Zug gibt es Wagen der ersten und der zweiten Klasse.
On this train, there are first- and second-class carriages.
Früher sagte der Stand einer Familie viel über ihre Möglichkeiten im Leben.
In the past, a family's social status said a lot about their opportunities in life.