Trying to Understand the Zoom

My Sony HX400V digital has a fixed Zeiss (branded) lens allowing me to "shoot unforgettable action with a 50x optical zoom (100x Clear Image Zoom)" etc. etc. I'm not sure exactly what that means, although Sony explains it this way:

Lens Type: Carl Zeiss Vario Sonnar T LensAperture: f 2.8 – 6.3

Optical Zoom: 50x

Focal Length (35mm equivalent):

Still 1:1: f=28.5-1425mm

Still 3:2: f=25-1250mm

Still 4:3: f=24-1200mm

Movie 4:3: f=32.5-1625mm (SteadyShot Standard) & f=34.5-2300mm (SteadyShot Active) or 38-2350mm (SteadyShot InteligentActive)

Movie 16:9: f=26.5-1325mm (SteadyShot Standard), f=28-1850mmmm (SteadyShot Active), f=31-1900mm (SteadyShot InteligentActive)

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Perhaps it would be possible for one of the technical experts here to give me a quick explanation in 25 words or less? I'm trying to understand this.

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Since I bought it, I've rarely used the zoom feature other than to take photos of whales and birds. This past weekend I tried it on some flowers:

Here's my position, and the arrow pointing at the flowers (which were more visible to the naked eye)
The data says focal length 4.3mm, f3.2and 1/60

The shot (not cropped or processed)
The data says focal length 215mm, f6.3 and 1/250

The non-zoom, non-crop photo where I walked over to the plants
The data says focal length 8mm, f3.2and 1/160

PuristS Proof of Authenticity
The data says focal length 4.3mm, f3.2and 1/250

Now I have just remembered a similar "long-reach" done earlier this year as part of my White Van Man postings.

The context from which my wife picked out a Borrego sheep with her very good eyes:

The data says focal length 4.3mm, f3.2and 1/250

The fully-zoomed photo as he came out from under the shadow of the rock
The data says focal length 213.6mm, f6.3 and 1/125

Cazalea

Photography

Trying to Understand the Zoom

Trying to Understand the Zoom

Re: Sony HX400V