Yes, both phrases essentially mean the same thing, which is to undergo a medical examination. However, there can be a slight difference in connotation based on the preposition used:
"To have a check-up" is a more general phrase. It simply means that a person is undergoing a medical examination, but doesn't specify where the examination is taking place. For example, as mentioned by the teacher before me, a doctor could come to the person's home to conduct the check-up.
"To go for a check-up" typically implies that a person is leaving their current location to visit a healthcare facility for a medical examination. This phrase might suggest the act of leaving home or work to visit a doctor's office, clinic, or hospital.
In most contexts, these phrases can be used interchangeably, and the exact location of the check-up is often clear from the broader context.