Learning C forces you to think harder about some issues such as explicit and implicit memory management or storage sizes of basic data types at the time you write your code.
Once you have reached a point where you feel comfortable around C's features and misfeatures, you will probably have less trouble learning and writing in C++.
It is entirely possible that the C++ code you have seen did not look much different from standard C, but that may well be because it was not object oriented and did not use exceptions, object-orientation, templates or other advanced features.
