The analytical engine wasn't a stored program computer. It most closely follows the Harvard architecture, with instructions read from punch card memory. The analytical engine's claim to fame is that it was the first Turing complete computer to be designed.
A stored program computer refers to the computer architecture where program instructions and data are stored in the same memory. This is also referred to as the Von Neumann architecture.
In contrast, a lot of early computers were built with separate instruction memory like punch cards. This is called the Harvard Architecture. If the instructions were immutable, which they usually were, then things like modifying the program at runtime were not possible.
Concrete examples of this difference is the Harvard Mk 1 and the Manchester Mk 1, the former being a Harvard architecture computer and the latter is a stored program computer or a von Neumann architecture.
"Babbage architecture" would have been much more accurate than "Harvard architecture", because Howard H. Aiken, the designer of Harvard Mark I, has been explicitly inspired by the work of Babbage into making his automatic computer at Harvard, which was intended as a modern implementation of what Babbage had failed to build.
The "Harvard architecture" had nothing to do with Harvard and it was not a novel thing. Having separate memories for programs and for data has been the standard structure for all programmable computers that have been made before the end of WWII, in all countries, and the methods for storing computer programs had been derived from those used in programmable looms and in the much earlier music boxes, which are the earliest programmable sequencers. Like the computer keyboards have a history of millennia since their origin in musical instruments (i.e. organs), the computer program memories have also their origin in (automatic) musical instruments, more than a millennium ago.
