The word "gospel" means good news or good message.

From a selfish viewpoint, the good news would be "my personal salvation in the sweet by and by".

From a universal viewpoint, the good news is the return of the King and His victory over Satan ALREADY! This will result in the restoration of all things, including ALSO ME. (And he that sat upon the throne said, Behold, I make all things new. Revelation 21:5)

The King is victorious! (gospel of the kingdom - big picture)

The "Gospel of the Kingdom" is the gospel Yahushua, the Christ preached. It is the only gospel He instructed His disciples to preach.

Matthew 4:23
And Yahushua went about all Galilee, teaching in their synagogues, and preaching the gospel of the kingdom, and healing all manner of sickness and all manner of disease among the people.

Luke 9:1,2
Then he called his twelve disciples together, and gave them power and authority over all devils, and to cure diseases. And he sent them to preach the kingdom of Yahweh, and to heal the sick.

But, the Messiah came to seek and save the lost (Luke 19:10). Isn't this a gospel of salvation?

Luke 19:10
For the Son of man is come to seek and to save that which was lost.

It is very easy for you and me to personalize this salvation (and we should) "He came to save ME"

But more was lost than just ME. Yahweh lost His kingdom, His government, His state, His position as Ruler.

If you think YOU are the most important thing lost, you are seeking your own life too greatly, which will result in its loss.

Luke 17:33
Whosoever shall seek to save his life shall lose it; and whosoever shall lose his life shall preserve it.

What do YOU think was more importantly lost? YOU? or the entire KINGDOM?

The Son came to seek and save that which was lost. This was His Kingdom (which happens to also include you and me). The seeking and saving of His Kingdom is the Gospel of the Kingdom also called the Gospel of Jesus. The seeking and saving of you and me is the doctrine of salvation, sometimes called a gospel of salvation (because it is good news) but it isn't the Gospel of the Kingdom.

The doctrine of salvation is about a Redeemer. The Gospel of the Kingdom is about a King! This is the Gospel Jesus preached and commanded us to preach - the KING!

For an analysis of the difference, see here