The bag the OP describes are ones that, when looking for patterns for them, seem to come under "sling bags". Sling bags do come in all shapes and sizes but seem to include the narrow, just hold the minimum, bags. I am hoping to start making some of these in the summer for Christmas presents. They can range in fabric from summer floral to tweed, leather, etc.
Because I am looking at these at the moment, I picked one up at our local market recently. I think it's ideal for walking. So, the main body is 18cm tall x 10 cm wide and has a top edge zip around the short side, long side, and second short side. Sitting on the front is a gusseted pocket with a flap and some nice bag furniture and popper to hold it shut. This part is big enough to hold a phone.
The main body has an accordion lining with a central zipped purse. The areas on either side are just big enough for a mini diary on one side and small essentials on the other. There are also three card slots on either side.
I like sling bags as they lend themselves to the practical. They can be made to carry water bottles, iPads, A4 folders or whatever you want. You can walk or cycle with them and have them either cross body or over the sholder or using a wrist strap. They can go to the back or the front. One of my favourites.