Hi and welcome to the forum
They both look gravid (pregnant). The spotty one looks like it will be giving birth in a couple of weeks. the orange one maybe a week later.
The fish are Xiphophorus variatus x Xiphophorus maculatus, and probably have some Xiphophorus helleri genes thrown in. This all goes back to the 1970s and 80s when the commercial breeders were hybridising fish to get more colour in them.
They are just common platies that resemble X. maculatus.
I don't know what the common name is for the spotty fish.
The orange and black fish is a red wagtail high fin platy. The red is from the colour of the body. The wagtail is the red/ orange body and black tail. The high fin is due to the elongated dorsal (top) fin.
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How long has the tank been set up for?
Did the shop tell you about the filter cycle?
What sort of filter do you have and is it run continuously (24/7)?
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MAKING THEM MORE COMFORTABLE
Both fish look reasonably healthy.
Most fish health issues are caused by poor water quality. Have good filtration, don't overfeed the fish, do regular water changes and gravel cleaning, clean the filter once a month.
Have some floating plants in the tank like Water Sprite (Ceratopteris thalictroides/ cornuta). These plants provide lots of hiding places for baby fish and for the mothers when they are giving birth. You can also plant the Water Sprite in the gravel and it grows into a lovely light green shrub type plant.
If you don't have a picture on the back of the tank, then put one on. You can buy aquarium backings from any pet shop or online. You just tape them to the outside of the tank. You can also use coloured card, a plastic bin liner, or virtually anything to make the back of the tank appear solid to the fish.
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TURNING LIGHTS ON AND OFF
Stress from tank lights coming on when the room is dark can be an issue. Fish don't have eyelids and don't tolerate going from complete dark to bright light (or vice versa) instantly.
In the morning open the curtains or turn the room light on at least 30 minutes (or more) before turning the tank light on. This will reduce the stress on the fish and they won't go from a dark tank to a bright tank instantly.
At night turn the room light on and then turn the tank light off. Wait at least 30 minutes (or more) before turning the room light out. This allows the fish to settle down for the night instead of going from a brightly lit tank to complete darkness instantly.
Try to have the lights on at the same time each day. Use a timer if possible.
