Yes it's the same word, it's the infinitive form of खाना, it is used in many situations, मैं खाने जा रहा हूँ = I am going to eat. And this form can be used with all verbs, मैं सोने से पहले खाऊंगा = I will eat before sleeping. I'm sure there is some rule for when to use करना and when to use करने, I just learned based on where I saw it used though, i.e. 'Going to do' is 'करने जाना', as well as if a preposition comes after the verb, as in मैं सोने से पहले खाऊंगा, से follows सोना so it becomes सोने. Another example: मैं हिंदी समझने में काफ़ी खराब हूँ = I'm quite bad in understanding Hindi, समझना is followed by में, so it becomes समझने. Hope this helped!