The principle of sufficient reason, due to Leibniz, states that there is always a reason why some particular thing happens, rather than some other thing. This does not immediately or obviously pose a threat to freedom. Note that "reason" does not mean the same as "cause", although a cause might be a reason.
Determinism states something much stronger, more complicated, and more sinister. It tells us that the laws of nature and the initial state of the universe at some time in the past entail the state of the universe in the present. Entailment is a strong relation, and what determinism means is that if the laws are whatever they are and the initial state of the universe is whatever it is, then the the universe must (nota been, "must") go into the subsequent state. There is a necessary truth. It is that if the universe is in the initial state, and the laws apply, then the universe will go into the second state. Determinism has been held to pose a severe threat to freedom in the metaphysical sense, or freewill, though so-called compatibilists have a view which de-fangs determinism, if it is successful.
The principle of universal causation is different again. It states that every event has a cause. This might well be false of the first event in time, if it really is the first event, because there is no prior event available to cause it, since nothing is prior to the first event.