Starting with your stated goal:
"I would like to be able to run my programs on any GPU."
Then yes, you should learn OpenCL.
In answer to your overall question, other GPU vendors do use different architectures than Nvidia GPUs. In fact, GPU designs from a single vendor can vary by quite a bit, depending on the model.
This is one reason that a given OpenCL code may perform quite differently (depending on your performance metric) from one GPU to the next. In fact, to achieve optimized performance on any GPU, an algorithm should be "profiled" by varying, for example, local memory size, to find the best algorithm settings for a given hardware design.
But even with these hardware differences, the goal of OpenCL is to provide a level of core functionality that is supported by all devices (CPUs, GPUs, FPGAs, etc) and include "extensions" which allow vendors to expose unique hardware features. Although OpenCL cannot hide significant differences in hardware, it does guarantee portability. This makes it much easier for a developer to start with an OpenCL program tuned for one device and then develop a program optimized for another architecture.
To complicate matters with identifying hardware differences, the terminology used by CUDA is different than that used by OpenCL, for example, the following are roughly equivalent in meaning:
CUDA: OpenCL:
Thread Work-item
Thread block Work-group
Global memory Global memory
Constant memory Constant memory
Shared memory Local memory
Local memory Private memory
More comparisons and discussion can be found here.