The difference is that prayer is directed toward God - in other words, at One who is outside of us. On the other hand, your friend's meditation is directed inward, at herself and her own thoughts and feelings.
To put it another way, true prayer is a conversation - a conversation with God. When we pray, we express our deepest thoughts and concerns to Him, knowing that He loves us and has promised to hear us. We don't try to empty our minds when we pray (as happens with some types of meditation); instead, we share our every concern with God - just as we would with a close friend (only more so). The Bible says, "In everything, by prayer and petition, with thanksgiving, present your requests to God" (Philippians 4:6).
Don't misunderstand me; the Bible does tell us to meditate on God and His Word - that is, to reflect on Him and His goodness to us, and think prayerfully about His will for our lives. But this doesn't involve emptying our minds; it involves instead prayerful thought and reflection. The Psalmist described the godly person in this way: "His delight is in the law of the Lord, and on his law he meditates day and night" (Psalm 1:2).
Pray for your friend, that she'll come to realize God's great love for her and give her life to Christ. And if you have never made your own decision for Christ, commit your life to Him today.