Module vs DynamicModule

Questions
,
1

This code works with Module, but not with Dynamic Module, I don’t understand why.

Clear[T, n];
Module[{T, n}, T = {};
 Print@InputField[Dynamic[n, {n = #;
      AppendTo[T, n]} &]];
 Print@Dynamic[T];

VS

Clear[T, n];
DynamicModule[{T, n}, T = {};
 Print@InputField[Dynamic[n, {n = #;
      AppendTo[T, n]} &]];
 Print@Dynamic[T];

It seems to be a problem with Print. Why doesn’t it behave as expected?
CellPrint works though.