Whether a lens is an FX or a DX lens, the actual focal length is always used. There are certain technical reasons why this is so, but the simplest is that a lens' focal length is defined as the distance from the film plane needed when the lens is focused at infinity to cast point light sources as a single point on the film plane. This doesn't change with regard to sensor size. What does change with regard to sensor size is the angle of view (AoV) or field of view (FoV) that a lens of a specific focal length will include in the part of the image circle that falls on the sensor.
What this means is that if you are using a 50mm lens on a Full Frame FX camera, the AoV will be about 46° diagonally. The same 50mm lens on a DX crop sensor body will have an AoV of about 31°. That is an equivalent AoV of about a 75mm lens on the FF body, and that is why camera manufacturers say that the 50mm lens on a crop body is a 75mm equivalent.¹ If you print photos taken of the same subject from the same distance using the same focal length lens with both a DX and FX camera on the same size paper, the image from the crop sensor camera will make the subject appear larger. This is because the ratio between the crop sensor size and the print size is greater than the ratio between the larger full frame sensor and the same print size, thus the magnification factor of the photo taken with the crop sensor body is higher when both are viewed at the same display size.
To understand the 35mm/FF equivalent FoV your 50mm and 55mm lenses yield on your D3200 and α6000, both lenses need to be multiplied by the crop factor, even though one of the lenses does not project a light circle large enough to fill a full frame sensor.
Both are APS-C sensors, and the Sony is shooting at 50mm and the Nikon is shooting at [effectively] 75mm. The Nikon should be far more "zoomed in," but isn't.
The Sony with the lens set at 55mm is shooting at [effectively] 82mm.
Your Nikon D3300 with 50mm FX lens is giving you the same angle of view that a 75mm lens will give on a full frame sensor. Your Sony α6000 is also giving you the same angle of view at 55mm that an 82mm lens would give on a full frame camera.
¹ There's no such thing as true equivalency when comparing disparately sized sensors. For a detailed discussion of this, please see this answer to Lens equivalent depth of field See also: Can a smaller sensor's "crop factor" be used to calculate the exact increase in depth of field?