A very good question!
Both words mean about the same but they are sometimes used in different ways.
'transfer' tends to have a more formal tone and 'move' is more down to earth. 'Move' is used much more often than 'transfer'.
"I moved house last week." (It would sound very strange to say that someone transferred house.)
"I couldn't move my leg."
"I transferred some money from my bank account to my credit card account." (You can also say "move money" instead of "transfer money".)
"The footballer transferred from Chelsea to Aston Villa." ("Transfer" here has a specific, technical meaning in sports management.)
Notice that both "transfer" and "move" can be used as nouns and as adjectives (they can modify another noun) as well as verbs.
"The move is expected to take place next week." (:noun)
"Get a move on!" (Colloquial/slang:=hurry up)
"You should fill in these transfer forms when you want to change to a different course." (:adjective)
"Manchester United football club paid a huge transfer fee when Smith moved clubs." (:adjective)
I hope this helps.
QUOTE: "The sign on the door of opportunity reads PUSH."