I don't know why everyone here is appealing to our intuitions about the English word "prayer". @Yishai @Fred

Some analysis of how roots like דרש בקש פלל שאל are used in Tanakh for God-targeted and human-targeted requests would be most welcome.

@DoubleAA I don't think it is a linguistic question. It is about what is the Halachic definition of prayer and what is asking someone to pray for you mean in that context. The OP only brought two cases in the end - asking a soul to pray for you and asking a soul for forgiveness.

@DoubleAA But the idea of prayer as a form of service to the target ("ועבדתם, את ה' אלוהיכם" (שמות כג,כה): מפי השמועה למדו שעבודה זו--היא תפילה") isn't in either of those two cases.