External visibility is public domain information for everyone to see, such as publications and patents.
Internal reputation is often proprietary and known only inside our institution, such as design or implementation for a product.
Our internal reputation is more important for the particular jobs (e.g., performance reviews and rewards), but that often contains confidential information which only a few colleagues can vouch for.
Both are important for our careers. For example, when we want to switch jobs, most people can only evaluate our external visibility and will require references to vet our internal reputation.
Thus, it is important to maintain a good balance of both.
I am lucky enough to enjoy doing both (e.g., publications and products).