Praying! Two "different" ways?

 A few weeks ago I had a discussion with someone on prayer, and based on Matthew 18:19 which says, "Again, truly i tell you that if two of you on earth agree about anything they ask for, it will be done for them by my Father in heaven." While I don't like to put labels on certain bible verses I remember from more than 25 years ago someone referring to this as "name it claim it prayer". I am not saying I disagree with the idea of ask for it and it shall be given to you, but I would add, "if it is God's will for me", then he will give it to me. I do believe that God gives us the desires of our heart, but I also believe that what we desire is not necessarily what God wants for us, simply because our desires are not always God based, but selfish based. Maybe I lack the faith to pray the "Name it, Claim it" prayer. I tend to be more like the persistent widow in Luke 18:1-8 which says, " And he told them a parable to the effect that they ought always to pray and not lose heart.  He said, “In a certain city there was a judge who neither feared God nor respected man. And there was a widow in that city who kept coming to him and saying, ‘Give me justice against my adversary.’  For a while he refused, but afterward he said to himself, ‘Though I neither fear God nor respect man,  yet because this widow keeps bothering me, I will give her justice, so that she will not beat me down by her continual coming.’” And the Lord said, “Hear what the unrighteous judge says.  And will not God give justice to his elect, who cry to him day and night? Will he delay long over them?  I tell you, he will give justice to them speedily. Nevertheless, when the Son of Man comes, will he find faith on earth?”
To me I see two quite different ways to pray. Neither one wrong, but more of where my prayer life fits in. I would love to hear comments from anyone on what they see in the New Testament regarding prayer."