I suppose I’ll inaugurate the answering of questions on this forum, although I’m not totally sure I understand the question. I’ll give it my best try.
Are the gospels synonymous in their content? No.
Are the gospels synonymous in that they all say the exact same thing? No.
Are the gospels synonymous in their purpose? I would argue yes. John and Luke clearly outline for us the purpose behind what they’ve written (Luke 1:3-4 and John 20:30-31) and although Matthew and Mark don’t come straight out and say why they’ve written, it seems like they also have a similar purpose.
Mark’s gospel begins by saying in verse 1 “The beginning of the gospel of Jesus Christ, the Son of God”. Matthew’s gospel seems to have less external writing (i.e. the author inserting a comment into the text) that would suggest his motivation for writing, but within the storyline it seems to me that a theme and purpose can be seen through the gospel. This theme and purpose relates to who Jesus is and what his gospel is.
Some of you are perhaps familiar with the teaching that the gospels are like four different perspectives on Jesus, just like four witnesses to an event would all tell it a bit differently. While that might be accurate, I feel it lessens the power of each gospel’s witness and testimony. The gospels were crafted and created, pulling stories from Jesus’ life, in an intentional manner, not a witness giving us a play by play of everything that occurred.
Each gospel is trying to get us (and even the ‘us’ can vary. Matthew’s harsh critique of religious leaders might be read very differently in a mostly affluent North American setting than it would be in a more impoverished Latin American setting) to see Jesus and his gospel. The authors probably weren’t planning to have their four gospels read together, one after the other, as we are prone to do. We try to line them up, but I’m not sure they were even meant to be lined up. To me, they line up in purpose, which I believe is articulated the clearest in John 20:31 “but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.”