A landscape designer is a person that designs landscapes, while a landscape architect is someone who has an academic degree in landscape architecture. There are also many job titles with "landscape" as part of the name such as land development manager, land developer, and landscaper. Landscape architects work at using science and math to develop new ideas for their projects which can be thought of just as design since it's not always about recreation or repurposing nature. A good example would be reorganizing the layout of a human population around water sources in order to increase natural biodiversity.
There's no difference between these two professions' skillsets, but there are some differences in career paths due to specialty.