In summer, it is not unusual to find an uchiwa or two somewhere around a Japanese home. Even one handed out at a shop or event with advertising printed on it may simply come home and get used. For many people, an uchiwa is not a special traditional object. It is just a familiar thing to pick up when the weather is hot.
A sensu creates the same kind of breeze, but the two are not really treated as interchangeable.
The most obvious difference is their construction. A sensu is a folding fan: it opens out from a set of ribs and closes into a narrow shape. An uchiwa is a rigid fan with a fixed flat surface and cannot be folded. That makes a sensu much easier to carry around.
A sensu is easier to carry, although carrying one throughout the summer is far from universal. Some people do carry one, but many do not. Uchiwa are also rarely carried around as everyday personal items. They are more likely to stay at home or be used somewhere they happen to be available.
The difference becomes clearer when you look at the situations in which they appear. Uchiwa fit naturally at summer festivals and fireworks displays, and shops or events sometimes give away inexpensive ones printed with advertisements. They have a casual, everyday image.
Sensu can also be used simply to cool yourself, but they have another side to them. They appear with traditional clothing, in tea ceremony and Japanese dance, and as gifts. In some settings, a sensu is not merely something used to make a breeze. It can be part of the clothing, the setting, or the etiquette surrounding an occasion.
That difference in atmosphere matters. Seeing a sensu at a somewhat formal event such as a wedding would not seem strange. Bringing along a promotional uchiwa covered in advertising, however, could look noticeably out of place. Both are fans, but they do not feel appropriate in the same settings.
This is not a matter of sensu being expensive and uchiwa being cheap. There are beautifully made craft uchiwa as well as inexpensive sensu for everyday use. The places they are used and the impressions they give are different enough that sensu and uchiwa feel like two fairly distinct objects.