Do apps on an SSD run faster even if windows is on a separate HDD? [closed]

Side note: I can't install windows on the SSD because it doesn't fit.

It will but the difference could range from barely perceptible to ten-fold! This depends what type of application this is. Any application needs to be loaded from storage to memory. SSD are substantially faster than HDD and so loading time is always faster. This will make a difference proportionally to the application size. Generally though, loading is not much of a concern for most end-user software since you it's startup time.

While running, the actual bottleneck varies between software. We say a software is I/O-bound when it spends most of its time waiting for I/O. For application that need to read or write large amounts of data, SSDs really shine. Most software for video editing and processing fall into this category since they work with much more data than can fit into memory. Working with gigapixel images and large 3D models also benefits enormously from an SSD.

Other applications, those that work in memory entirely once loaded will see much less improvement since they do not require much I/O bandwidth. It is the data that matters though. Some applications are fairly small but let you work on large files, in which case you will get a huge benefit from simply moving your data to an SSD. The application itself can remain on a standard HDD.

SSD truly brought a huge leap in performance compared to traditional HDD and so some applications really see a dramatic improvement. Very few technologies have surpassed their predecessors by so much yet this has happened again recently with NVMe. A typical SSD is 5X faster than a HDD and NVMe is 10X faster than SSD. I recently replaced my system and VM SSDs with an NVMe RAID and experienced a huge improvement.