"Jesus gives them no new form of prayer. That which He has before taught them He repeats, as if He would say, You need to understand what I have already given. It has a depth of meaning you have not yet fathomed. MB 103.1"
"After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name."
The EGW passage directly refers to the prayer taught in Matthew 6:9, indicating an explicit allusion. The context makes it clear that she is discussing the Lord's Prayer.
"The Saviour does not, however, restrict us to the use of these exact words. As one with humanity, He presents His own ideal of prayer, words so simple that they may be adopted by the little child, yet so comprehensive that their significance can never be fully grasped by the greatest minds. We are taught to come to God with our tribute of thanksgiving, to make known our wants, to confess our sins, and to claim His mercy in accordance with His promise. MB 103.2"
"Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God."
Both passages discuss prayer and making requests known to God with thanksgiving. Philippians 4:6 is a clear instruction to present requests with thanksgiving, and the EGW quote echoes this by mentioning thanksgiving, making needs known, confessing sins, and claiming mercy. The EGW passage expands on the elements of prayer mentioned in Philippians.
"If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness."
The EGW passage directly mentions confessing sins and claiming mercy, which aligns with the principle of 1 John 1:9 regarding confession and forgiveness.