The RUP puts "Business Modeling" as a step before "Requirements Modeling". This means, during business modeling, one describes business processes in their current state, often mostly technology agnostic.
For example, when I run a company for selling new houses, there might be a business process of showing prospective buyers images of comparable houses or images of their living rooms. A business process model will capture this process, but usually not tell you if the images are in some paper catalogue, or created in a computer interactively.
When it comes to requirements, however, one moves a step towards developing of business software or IT systems - here we collect the use cases which shall be supported, improved or changed by such a software or system, together with textual descriptions of what the - yet to be developed - system shall provide or do. This is usually a step less abstract than the business modeling step, but still not as low-level as the next RUP step "Analysis & Design".
In the former example, the (high-level) requirements may describe a computer system where 3D models of a house and its rooms are created interactively by the sales person together with some customer, which can be shown, for example, on a standard PC monitor, or maybe with a VR headset. This is the same process as before, but on a more detailed level of abstraction and focussing on the system to be developed.
Hence, it is not surprising that in both stages you find the same terms like "use case" or "actor", or that you can utilize tools like process diagrams or use case diagrams for both. It is not the form which makes a difference, but the content.