No. They are related but they're not the same.
In "The Angels Take Manhattan", for example, the Eleventh Doctor had no regenerations left (as he eventually explained in "The Time of the Doctor") but he did have enough regeneration energy to heal River Song's broken wrist. Other stories, such as "The Twin Dilemma", have also shown that a Time Lord can have regeneration energy without being able to regenerate successfully but none has given a clear explanation of the process.
From "Journey's End", we know that the process of regeneration occurs in (at least) 2 phases:
- First, regeneration energy repairs any damage to the Time Lord's existing body (& "The Time of the Doctor" showed that this can even rejuvenate that body). The Eleventh Doctor called this phase "the reset".
- Second, it rebuilds the Time Lord's body into a new one.
The Tenth Doctor managed to interrupt the process before the second phase could occur but he explained that he was able to do so only because of special circumstances (the presence of his severed hand, into which he could dump the unused regeneration energy).