Not really computer architecture as a computer involves the peripherals and PCB and perhaps the chassis, buttons, connectors, etc.
The instruction set architecture is the architecture, the look and feel of the thing. Just like the architecture of a building. The instruction set is the set of instructions that implement that architecture. (as Brendan has pointed out you can have more than one set that implements the same architecture). A good example is ARM, ARMv7-m defines the architecture for some/most of the cortex-m (the marketing name for a product family) cores. The cortex-m3, cortex-m4, cortex-m7 conform to the ARMv7-m architecture which is defined in the ARM Architectural Reference Manual for the ARMv7-m. But these are different cores, they may be complete rewrites from scratch, they may have different depth pipelines, one might have a cache and/or fpu where another doesnt. In this case there is an instruction set defined by the architecture that they all conform to (the fpu is an exception in this case and not defined in the architecture).
An architect may design the building or building guidelines for a McDonalds and when you drive by you look at that building and without looking at the logo you know it is a mcdonalds or a wendys or a pizza hut. But not everyone of those buildings was built by the same construction crew using lumber from the same mill or paint from the same vendor, etc. The instruction set architecture defines the architecture and probably the instruction set the machine code it implements but the specific chips or cores made to conform to that architecture might not be identically built, on the surface the architecture looks the same, it looks like a Taco Bell, but it may be built differently than a Taco Bell in the next town over, you can still buy tacos that taste pretty much the same when you use that facility. As far as the machine code/instruction set goes programming two different cores from the same architecture look and feel the same, the tacos taste the same. But the implementation may be different (they might put the tomatoes in before the sour cream instead of after).
Good, bad, or otherwise, the two terms are often used interchangeably to mean the same thing (the instruction set, the possibly machine code instructions for the thing being talked about).