If other people are also wondering about this, I am doing research on this question and this is what I understood so far.
The algorithms may differ, but the main idea is indeed the same.
I think the difference comes from different research communities and their history.
Regionalization is used by researchers focusing on vector-based GIS and usually belonging to the spatial statistics community. Image segmentation comes from the image processing community, which includes spatial scientists focusing on raster-based GIS, surveying/remote sensing and GEOBIA.
For both, the goal is to create more pertinent objects in order to improve their analysis (because of the MAUP in spatial statistics and for improving image classification for surveyors).
The paper on the MRS algorithm in eCognition and the work of Blaschke are interesting for image segmentation. See cluterPy for a list of algorithms on regionalization, with references. I believe the work of Openshaw is seminal on this question in spatial statistics.
Not that many people are making the connection, because, I guess, this is a question for ultra-specialists in both communities. Firstly, these concepts may be old (70's for regionalization, even before for image processing), the development of performant implementations started only fifteen years ago. Secondly, it is still not so easy to find performant tools for using these algorithms. So these concepts are not really widespread. There is a tool in ArcGIS for regionalization in the last updates. Ecognition is widely used for segmentation. The best free segmenting tool I found and could use is i.segment in Grass (which used the MRS algorithm). As far as I know, there is no implementation of regionalization algorithms like cluterpy in free GIS software and there is no library like clusterpy in R.
ps. People are also using spatially constrained clustering for regionalization.