bagging vs. pasting in ensemble learning
Actually I think that you are mostly correct, except that in my understanding &quot;with/without replacement&quot; applies only to selecting one subset, not across subsets. This means that if we have a training set of instances $T=\{t_1,..,t_N\}$:

With bagging, a particular sample can contain duplicate instances, in other words it is not a subset of $T$ but a multiset where an instance $t_i$ may occur several times. Of course the probability to pick the same instance $t_i$ $n$ times decreases quickly when $n$ increases, depending on the size $N$.
With pasting a sample is a subset of $T$ and cannot contain the same instance $t_i$ twice. However another sample is drawn again from the full set $T$, which means that it is possible for an instance to be selected in several different samples.

In theory, the size of a sample can be higher than $N$ with bagging but not with pasting.
Note that I'm referring to multiset for the sake of clarity but formally $T$ itself is not a set since in theory it may contain the same instance twice.