In Pascal, Integer (signed) is the base type. All other integer number types are a subranges of integer. (this is not entirely true in Borland dialects, given longint in TP and int64 in Delphi, but close enough).
An important reason for that if the intermediate result of calculations gets negative, and you calculate with unsigned integers, range check errors will trigger, and since most older programming languages DON'T assume 2-complement integers, the result (with range checks off) might even be corrupt.
The THandle case is much simpler. Delphi didn't have a proper 32-bit unsigned till D4, but only a 31-bit cardinal. (since 32-bit unsigned integer is not a subrange of integer, the later unsigned ints are a subset of int64, which moved the problem to uint64 which was only added in D2010 or so)
So in many places in the headers signed types are used where the winapi uses unsigned types, probably to avoid the 32th bit getting accidentally corrupt in those versions, and the custom stuck.
But the winapi case is different from the general case.
Added later Some Pascal (and Modula2/3) implementations circumvent this trap by setting the integer at a size larger than the wordsize, and require all numeric types to declare a proper subrange, like in the below program.
The first holds the primary assumption that everything is a subset of integer, and the second allows the compiler to scale nearly everything down again to fit in registers, specially if the CPU has some operations for larger than word operations. (like x86 where 32-bit * 32-bit mul gives a 64-bit result, or can detect wordsize overflows using status bits (e.g. to generate range exceptions for adds without doing a full 2*wordsize add)
var x : 0..20;
y : -10..10;
begin
// any expression of x and y has a range -10..20
Turbo Pascal and Delphi emulate an integer type twice the wordsize for their 16-bit and 32-bit offerings. The handling of the highest unsigned type is hacky at best.