Main difference between Soul/Funk/R&B
"R&B" ("Rhythm and Blues") was a term coined by then-journalist Jerry Wexler of the industry-trade publication Billboard Magazine in 1948. The term "R&B" was first used by the radio and recording industry in the USA to describe all recorded music marketed to African-Americans. The term that "R&B" replaced was "Race Records" meaning records marketed to the minority African-American race. "R&B" was not originally a term that any musicians or bands used to describe themselves or their music. So when the term was created it did not describe any genre per se. It described nothing other than a specific marketing plan used by record companies and radio stations in that era.
Any artist or band in that era wouldn't spend any time thinking about whether they were "soul" or "R&B"; they would just make music and try to get it sold and earn income through the record business and radio business.
"Funk" is a little different, because to the best of my knowledge there was never an actual recognized commercial radio format in the USA called "Funk". Funk is a distinctive style that originated in the 1970s, usually characterized as African-American popular music with an emphasis on a certain distinctive heavy beat. There were bands that identified themselves as funk bands back in the day.
It would be correct to say that "R&B" encompasses all popular music made by African-American artists and marketed to the African-American public. "Soul" and "Funk" are each subsets of the larger category of "R&B".
For full background information and references that demonstrate the points I've just made, please read my previous answer to this question: