What are the differences between the following?
- He is planning to do something.
- He is planning on doing something.
When to use each?
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,
Coming after sentence two, an appropriate follow-up comment might be,
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:
On the other hand, suppose the whisperer said, with an emphasis on the word do,
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!
Although common usage may blur the lines, I believe "plan to" is used to communicate the plan itself, while "plan on" is used when describing the assumptions or predictions on which the plan is based or depends.
The first sounds logical because is planning shows an action going to be performed in the future, thus the first part is correct and regarding the second part, to do something is the infinitive. On the other hand, on doing something does not sound logical.