In addition to the Max Demakow's words, I would like to say that "беседа" implies as a rule a long conversation, in contradistinction to "разговор", which can be both short and long. Moreover, "беседа" as a rule implies a pleasant conversation, this word is very rarely used with adjectives which mean something unpleasant. "Разговор" can have all shades of senses: неприятный, непростой, тяжёлый, лёгкий, мимолётный, весёлый, интересный, познавательный, etc.

in fact, there is no difference. it's just a variation of synonyms. difficulties can arise in how they will change in numbers and time. например: вчера я случайно услышал разговор двух молодых людей в парке. или: я слышал, о чём беседовали эти люди в парке.

"Беседа" it's like small talk) more informal and casual. "Разговор" - if you have a topic or question which should be discussed. but basically, both are synonyms

беседа more friendship, разговор more official, but difference is a little. but I can't say that я беседовал с полицейским, который меня остановил для проверки документов. in formal and official ways where is subordination and role I can't say беседа

I can add that "беседа" sounds more poetic and we don't often use it, "разговор" is used much more often. Moreover, "беседа" can be about some philosophical, religious and other issues of that kind. "Разговор" is normally about casual things.