The name.

With Kate on this, they should be the same thing. I always bring external factors into my risk assessments such as environmental issues, other employees, items in the general vicinity as all these items can have an impact on the risk and as far as I am concerned, a JHA is just another name for it.

In the UK, we call this JSA, or Job Safety Analysis. This is where you break down a job into a sequential order of specific tasks within the job, which you then can risk assess.
In some more advanced manufacturing industries (eg automotive), someone has already done this in terms of a SOP (or Standard Operating Procedure, or just standardised work, if you are Japanese), which makes doing a risk assessment a whole lot easier, because it is very clear what the task and job actually entails. These usually have pictures of the activity in, or sometimes even videos. In these cases, a lot of variation has been taken out of the job because everyone is (or should be) doing it the same way every time. With variation comes possible error, not only from a health and safety perspective, but also a quality assurance one.

As Kate says, the only difference should be the name, as surely we should think about tasks that we risk assess in such logical steps? In the best JSA's, you can combine the two things, and then add environmental factors in, as has been suggested.