With cloning you get an exact copy, at least in terms of DNA sequence. This is done by copying a body cell called a "diploid cell," which has a full copy of an individual's DNA.

With parthenogenesis, you do not get an exact copy. You take two haploid gametes, aka sex cells, and implant one into the other similar to how a sperm implants into an egg. The difference is that in this case, it is two egg cells ("oocytes") from a single mother instead of a sperm and an egg from two different parents.

Most genes (with a few exceptions, particularly for male offspring) consist of two copies, one from the father and one from the mother. The grandfather and grandmother of the parthenogenetic offspring.

Whereas the mother has one copy each from the grandmother and grandfather (again, with some exceptions) the parthenogenetic offspring might get two grandmother copies, or two grandfather copies, or it might be the same as the mother with one copy of each. However, with how many genes there are, there is essentially a zero% chance the offspring gets one of each for every gene like the mother has. Thus, its DNA is different from the mother.

This is the same reason you are not a genetic copy of your brothers and sisters. In this case, there are 4 grandparents and 4 possible parings instead of 2 grandparents and 3 pairings for parthenogenesis.

Edit: perhaps an easier way to explain this. If two clones or two identical twins were to mate, their offspring would be genetically identical to parthenogenetic offspring. It is the most extreme form of inbreeding possible, but each offspring would still have unique DNA like brothers and sisters are unique from each other.