Not necessarily. I think the 8088 processors were out when I bought my 8086. Its real value was the education in MSDOS.
You are both probably right.
Speaking of the processor chips themselves, the 8086 was out first.
Then they designed the 8088, which had all the 8086 internals but was in a smaller package with fewer pins and a narrower external bus. This allowed designers to make a cheaper system overall, at the expense of a slower bus and thus lower performance.
The first IBM PC was basically a cookbook design from Intel’s literature, using the 8088.