でも meaning even/but/however is the て form of the copula です. The て form can allow you to do many things, but the most basic use is that it allows you to join to clauses together. You can think of it as meaning "and." も is the inclusionary particle which you use when you want to say "also" or "in addition too."
An example of でも would be 先生でも間違{まちが}います。Even a teacher makes mistakes.
You could use でも to state where an event took place as well. Do recall that も is the inclusionary particle though and you must use it when you are talking about similar topics.
If a topic of the activity "having fun" were already introduced at a certain location then you could state that you also "had fun" at another place.
プールでは遊{あそ}んだ。 X had fun in/at the pool. (Topic is introduced by は, verb is playing)
ジョンの家{いえ}でも遊{あそ}んだ。 X ALSO had fun in/at John's house. (Topic, which is another location, is marked by も, verb is playing)
If you did something other than "have fun", say "eat", then you would not be able to use the も particle.
So to answer your question, yes they do mean to different things but when you break them down into their separate parts, they are quite simple and easy to understand.
To anyone else who sees this and knows more than me, please correct me and go easy on me as this is my first time answering a question. (If I am incorrect with anything)