Somehow on the contrary there is much difference, sometimes even in the sense in which these two are used.
("logical") positivism (so called "logical empiricism" or "scientific empiricism"), a movement associated with the Vienna Circle.
Their mission was to 'unite' the science (especially as opposed to metaphysics) and give a correct sketch, description of scientific method (to dispute metaphysics). Their task concerned both scientific theory and language. This movement can be seen as empiricism (which states for example that they are in agreement with the methodology of natural science, and in that they believe that the source and origin of all knowledge is experience) and with a very important role for the (formal) logic "to describe the structure of permissible inference"(linguistic and logic). They are in agreement with empiricists that the origin of all knowledge is experience but they also seek for a "logic of science" with a very unique "authority", which in its turn leads to conformation theory.
To be direct, positivism states that 1) the only authentic knowledge is scientific knowledge[a uniqueness statement] (but empiricism is about source and origin of knowledge, which states that the origin of all knowledge is sense experience, and of course scientific knowledge is included). 2) this authentic knowledge comes from a special and unique method (scientific method) that is empiricism + specific principles of logic.
It asserts something about authentic knowledge and the method of achieving this authentic knowledge, empiricism is about, what is the basis of all our knowledge, it emphasizes experience and evidence (especially sense perception) to acquire knowledge, to use Kant, the "only knowledge we can have" is a posteriori (based on experience).