Qualcomm has their own system on chips (SOC) family named Snapdragon. Every Snapdragon SOC includes a CPU and a GPU.
Currently, their Snapdragon platform has 3 categories of SOCs available on the market: S1, S2 and S3, aiming at entry-level, mid-range and high-end devices respectively. All of Qualcomm's current SOCs are built on Qualcomm's proprietary CPU architecture called Scorpion (single-core Scorpion for S1, S2 and dual-core scorpion for S3).

In brief, Snapdragon is the name of Qualcomm's SOCs family and Scorpion is the architecture behind their current CPUs. You should know that the next generation of Qualcomm Snapdragon chipsets (S4) will use a new core architecture called Krait instead of Scorpion.

To answer your question more clearly:
A 1 GHz Qualcomm Snapdragon MSM8255 refers to a SOC with a single-core Scorpion CPU and Adreno 205 GPU.
1GHz Qualcomm Snapdragon can refer to any Snapdragon SOCs with a CPU running at 1GHz.
And lastly, 1GHz Scorpion CPU only means that the CPU inside a SOC is based on Qualcomm's Scorpion architecture and operates at 1GHz.

As such, they are not the same. And yes, you need to know all this in order to get the right phone for your purpose.
As Qualcomm has already clearly listed their SOCs in 3 categories (S1, S2 and S3), you can easily choose the right phone. For instance, the SOC you mentioned (MSM8255) is listed under Snapdragon S2 class (this SOC is found in the HTC Desire HD, Sony Xperia Arc), so it is a mid-range SOC. If you really want a phone for gaming, S3 devices will be more suitable (such as HTC Sensation, Evo 3d, Rezound, etc...).