Ja, the UH-1H has the tail rotor on the left side and the A1 is on the right. The A1 tailboom also has a 'boot' in the tail, accessed on the right hand side.
Just to try basically clear up the whole Huey thing, they started out as the Bell 204, the stubby Huey, which the military designated the UH-1A, and following variations were the UH-1B, UH-1C, UH-1E, and UH-1F. In that time somewhere came the 'extended cab' version, fitted with a -11, called by the military the UH-1D, and the -13 version, called the UH-1H.
Agusta at some point in time also built the Huey, and they were called Agusta-Bell 205's, and then Bell built civillian versions called the 205 A1. It can get quite confusing....
The Hueys can be upgraded with engines, transmissions, drivetrains etc to make them better. The UH-1H's tail rotor is not lekker so people often retrofit them with 212 bits, tractor tails, fast fins, composites etc. The most common fit is to put a 212 42 degree in, as the 205 gearbox needs to be inspected every 400 torque events, quite a mission if you are doing that every 2 days or so!