There is a cooking terminology difference between the two, yes, particularly in the US. If something is "minced" the implication is that it's chopped very finely with a knife or blade, either manually or with a machine like a food processor. It's much less common to use the term "mince" in the US to refer to meat that has been put through a grinder, which is referred to as "ground". Grinding is a combination of pressing, cutting, and extruding to achieve a relatively uniform result.
I generally do not see the term "minced" used to refer to "ground" meat in the US at all (in the UK, "minced" is the standard term).
"Ground" is used for all sorts of products put through a grinder.
As noted, "ground" does not refer to the land in this case (note that "you're grounded" actually does refer to the land as it comes from the aviation-related terminology of being prohibited from flying). It is an adjectival usage of the past tense of "grind". The dictionary linked here includes the definition:
b) American English to cut food, especially raw meat, into very small pieces by putting it through a machine SYN mince British English