Good question... :thumbup: The simple answer is yes, they are trying to describe roughly the same engine.
The "in-line 4" refers to how the cylinders are oriented. In this case it means all 4 cylinders lie on the same plane or in a row instead of a V-8 or V-twin where the cylinders are anywhere from 45 to 90 degrees relative to one another (probably other angles too).
The "4 stroke" refers to how the engine produces power. There are lots of different ways but the most popular on a motorcycle are 2-stroke (mostly off road bikes these days) and 4-stroke.
The 4-stroke specifically refers to the 1.intake 2. compression 3. power and 4. exhaust strokes. Each step takes 1/2 of a full revolution (or 1/4 of a power revolution for the gear heads). The 2-stroke makes the process more concise and is much more powerful for the weight of the engine but not fuel or environmentally efficient.
Bottom line is both the FZ6 and FZ6R are both in-line 4 cylinder, 4 stroke engines. I'm not sure about the rest as for which has more power, higher compression ratios, or larger bore or stroke etc... Maybe someone else can help with other details.