Well, have a closer look and you'll find there are quite a few differences, in spite of their similar meaning. "Meet" can take an object, but if the subject is plural then you can treat the verb as intransitive. "I'll meet you later." "Let's meet later." It can also suggest a first time ("Nice to meet you" sounds very strange if you already know the person), and has a friendliness about it. Basically, you use "meet" for people. When a student says - incorrectly - "I met a difficulty", I reply with "Oh, hello difficulty!" The noun form is "meeting" ("meet" as a noun is only for sports). It comes from an Old English verb, and is suitable for common speech. "Encounter" always needs an object. You encounter something or someone... and as other members have said, it can suggest by chance or something unusual. Several dictionaries say it can be intransitive, but I'm trying hard to find a real example of this. If you take the above examples of "meet" and use "encounter" (eg. "Nice to encounter you") then they are simply wrong... and comical. However, "I encountered a problem" is correct. Encounter comes from French/Latin, so it works with a formal business style. It sounds strange and fancy in regular speech. It is originally a noun: an encounter. If you're still following all this... let's add "with". :) "Meet with" is slightly indirect, so now you can use non-human objects as well. "I met with a difficulty" is acceptable here. "Meet" is still a verb. "Encounter with" only makes sense if "encounter" is a noun. It is never a verb if "with" follows. The full phrase is "to have an encounter with X". Do a search and you'll find plenty of examples.

Encountering something is usually unexpected. We don't say "encounter with".

face to face meeting calls meet and encounter means bychance collision

Meet is more likely to describe many or alot of people or events. Versus encounter is more likely to descrie a single event or single person. Both words can be use interchangeable. The american language is full of words that can be use and interchange.