var means Variant, it can store almost any datatype.
Godot's core types used C language standard C99, such as uint8_t,uint32_t,int64_t, etc.
And, including C99 datatype, Variant type can store those list below:
- Container type: Vector List Set Map
- String
- StringName
- Math types: Vector...
- NodePath
- RID
So, var i meaning i can be int, uint8, String, Vector2i ... except for you specify a type explicitly, or use type inferred symbol :=.
var integer: int = 99
var another := 99
###### below one will cause error:
###### Parse Error: Value of type "String" cannot be assigned to a variable of type "int".
another = "pine"

Ref.
- godot\3.5.1-stable\core\variant.h
- godot\master\core\variant\variant.h