Was Kerrigan's Leviathan fought in Wings of Liberty?

In Heart of the Swarm, the Leviathan that serves as Kerrigan's command ship is completely massive

It is well known that the game can shrink down large ships to fit on the battlefield (most commonly seen with Battlecruisers). Is there any lore to speculate that this is the same Leviathan that was faced at the final mission of Wings of Liberty?

No, Kerrigan's Leviathan is not the same one that was shown in Wings of Liberty. The WoL Leviathan is killed by Raynor's Raiders (either in Shatter the Sky or in All In (vs Air), while Kerrigan's Leviathan is, by the looks of it, pretty much alive.

From what I read on the Starcraft Wiki and in the lore. Like the battlecruisers, the Leviathan looks to be all the same and are all classified class-10 zerg flyers.

However, it is my guess that, like battlecruisers, certain broodmothers might be able to "upgrade" their leviathan with new things to make then harder to kill or make them "punch" harder.