Daniel B. answered 09/02/23
PhD in Computer Science with 42 years in Computer Research
a.
Computers called 'mainframes' are typically used for business applications.
Namely those involving movement of a lot of data, calling for extra level of reliability.
They could be used for 'complex, sophisticated mathematical calculations', but not necessarily.
Such calculations usually call for large amount of parallelism, achieved by 'supercomputers'.
And those lately rely on GPUs.
b.
It is possible that some people do use those two terms interchangeably, but I have not heard that, and
I would find it confusing.
A 'port' is on a device, and a connector plugs into a port.