It can be a bit confusing (it confuses me!) so I'll explain in a bit more detail.
In 1970 a new rate of Fleet Chief Petty Officer was introduced, ranking with Warrant Officer Grade 1 in the Army and Warrant Officer in the RAF. Their beret badge was the one on the left in your initial posting.
In 1985 the Fleet Chief Petty Officer title was changed to Warrant Officer to bring them into line with the other services.
The design chosen for the beret badge for Fleet Chief Petty Officers (later Warrant Officers) was a more elaborate version of the Chief Petty Officer's beret badge. In practice, this was eventually seen as unsuccessful and, in 1990, a new design was introduced, which brought the beret badge closer in appearance to the Officer's beret badge. This is the third badge you posted.
From 1st April 2004 RN Warrant Officers became known as Warrant Officer Grade 1. This was made necessary by the introduction of the substantive rate of Warrant Officer Grade 2 for RN Artificers and technicians which replaced the existing non-substantive rate of Charge Chief Petty Officer (CCPO). Both grades of Warrant Officer wore the same cap and beret badges.
In June 2013 it was announced that the rate of Warrant Officer Grade 2 in the Royal Navy was to be phased out from December 2013, with no new promotions, although ratings holding the rank of WO2 would retain the rank until they were either promoted or left the service.
In 2020 it was announced that the rank of WO2 would return to the Royal Navy from 1st April 2022. It was brought back to allow the rank of WO1 to be held purely by men and women in positions which perform an executive, command and leadership type function. The aim is to 'restore the status of WO1 as the pinnacle of the ratings structure and a post everyone should aspire to', while the returning WO2 rank will embrace all branches and specialisations in the Royal Navy.
It's all quite straightforward really!
Hope it makes sense
Pete