Your question has largely been answered by others. (i.e. a 'path' isn't necessarily a public right of way. Indeed, it almost certainly isn't).
However I will point out that the best place to check up on the status of public rights of way (if that's what they actually are) isn't on OS maps but on the website of the relevant council, as it's those councils which are legally responsible for maintaining up-to-date records of such paths, rather than the OS. (In rural areas that's generally a county council. Elsewhere it might be a metropolitan council or a unitary authority). You'll probably then need to work out which parish the relevant path is in before you can consult the map.
To find such maps, google 'definitive map public rights of way', together with the name of the council. For example, if I do that for my home county of Suffolk, I end up here:
https://www.suffolk.gov.uk/roads-and-transport/public-rights-of-way-in-suffolk/view-definitive-maps-of-public-rights-of-way/
Clicking through to my local parish takes me here:
https://www.suffolk.gov.uk/assets/Roads-and-transport/public-rights-of-way/Needham-Market.pdf
(One needs to click the 'zoom in' button several times to be able to view the map clearly).
The symbols used on such maps are the same across the whole of the country and are shown here on the Gloucestershire County Council website:
https://www.gloucestershire.gov.uk/media/1520494/mainreception-userguidejun18.pdf
The definitive maps held by councils don't show permissive footpaths and bridleways though. They only appear on OS maps (or on maps from 'unofficial' sources, such as those drawn up by local walking groups).
The symbols used on OS maps, together with their meanings, are shown here:
https://www.ordnancesurvey.co.uk/newsroom/blog/right-to-roam-public-rights-of-way