meaning

The sentences are quite similar. They convey similar meanings. Without being overly technical (not that I'm capable of it), I suggest sentence number one sounds more definite than sentence two.

An appropriate comment coming after sentence one might be, for example,

"[He is planning to do something.] We are not sure what he is planning, but we know he's going to do something!"

Coming after sentence two, an appropriate follow-up comment might be,

"[He is planning on doing something.] We are not sure what he is planning, and we are not sure he will actually do it, but we are pretty sure he will at least make an attempt to do something."

In other words, sentence one is less "qualified-sounding" than sentence two.

The nonverbal aspects of the sentences, however, can affect the meaning and implication of the sentences. Let's say, for example, two people are whispering to each other in an audience that is gathered to watch a magician. The magician is on stage, and as he pauses briefly, as if to think what to do next, one person whispers to the other, with the nonverbal emphasis on the word something:

"He is planning on doing something!"

On the other hand, suppose the whisperer said, with an emphasis on the word do,

"He is planning to do something."

Which sounds more definite to you? If you say "Sentence two," you are probably well on your way to understanding the differences between the two locutions. If not, then I have failed to 'splain things well enough!