Does Jesus have two kingdoms? Do the two verses below signify that there are two kingdoms of Jesus Christ? If so, what are differences?
The kingdom of heaven

Matthew 16:19 (NKJV)
19 And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed[a] in heaven.”
Footnotes:
Matthew 16:19 Or will have been bound . . . will have been loosed

The kingdom of David

Isaiah 22 (NKJV)
The Judgement on Shebna
22 The key of the house of David
I will lay on his shoulder;
So he shall open, and no one shall shut;
And he shall shut, and no one shall open.
23 I will fasten him as a peg in a secure place,
And he will become a glorious throne to his father’s house.
Short answer: no. He does not have two kingdoms currently.

John 18:36 

"Jesus answered, My kingdom is not of this world: if my kingdom were of this world, then would my servants fight, that I should not be delivered to the Jews: but now is my kingdom not from hence." (KJV)

Jesus' kingdom is, for right now, not on earth. His kingdom resides in the heavenly realms and in the hearts of believers. You cannot grab or feel His kingdom right now. 

However, there is coming a time after Satan is cast into the lake of fire that Jesus will have a graspable kingdom.

Rev 21:10 

"And he carried me away in the spirit to a great and high mountain, and shewed me that great city, the holy Jerusalem, descending out of heaven from God" (KJV)

The Bible goes on after this verse to describe the city with the author's sight, such as sparkling, and the author goes on to give dimensions. This is clearly a kingdom able to be seen and felt. A graspable kingdom.

So the long answer is: Jesus has two different kingdoms, but only one right now.