What's the difference between a nebula with a filter and a nebula without a filter with an astronomical telescope?

The nebula filter is used to make you see the nebula more clearly. Astrophotography is also often used to connect it to the back end of the telescope eyepiece.

You can see the nebula without the nebula filter, but you can see it more beautifully with the filter. Of course, some nebulae can only be seen by adding filters, which means that filters can let you see more nebulae.

Nebula filters are generally narrow-band filters, which means that only light in a small wavelength range can pass through. For example, the common nebula filter is OIII filter, which can only let light near 5000 angstroms (that is, a small part of blue-green light) pass through. Because the light emitted by the nebula is concentrated in this frequency band, after this, the light emitted by other objects (such as stars) is weak, and the light emitted by the nebula is much weaker, so the nebula becomes prominent.