I would say that they are the same, but I am from America and have never heard anyone use "In future" in conversation. I can say that "in the future" does not means the same thing as "from now on". "In the future" means you are not going to begin now, but at a later point in time. "from now on" means that you are going to start something at that moment and continue with it. Grammatically, "In the future" would be future tense, while "from now on" would be future progressive.

不远处的, I looked this up for you in the 20 volume Oxford Dictionary. In future It is defined under the section for 'future' when it is used as an adjective. It is considered an elliptical or absolute form of the adjective. In future (time) The definition is ....that is to be, or will be, hereafter. In other words "from now on." In the future the word "future" is a noun here, with the meaning "the time to come, or future time." British Usage 'in future' in British English means "from now on" 'in the future' in British English means "at some point in time in the future" In future I will pay the rent.......From this moment on I will be paying the rent. In the future I will pay the rent.......Some day you will start to pay the rent ( we don't know exactly when) Man will live on Mars in future.......This is false because man is not living there now. Man will live on Maris in the future.....This may be true many years from now. American usage. The American Heritage Dictionary agrees with the above definitions. Webster's dictionary recognizes no difference in usage between 'in future' and 'in the future'