Any (M)ILP can be transformed to an equivalent (M)BLP.
There are multiple methods to do so, some described in this book.
The pure discrete problems are NP-hard just like their mixed integer cousins.
One method is to replace integers by a sum of binary variables per integer, the cardinality of which depends on each integer's span.
In practice, BLPs tend to be slightly easier to solve because binaries allow us to take many algorithmic shortcuts.
Mixed-integer/mixed-binary problems are of the same complexity. In practice, they are often harder to solve because we can't use the same reformulations that apply to pure discrete problems, and the complexity of branching on continuous variables is much worse than creating branch-and-bound trees of discrete variables.
Note however that "harder" here is ambiguous and should be taken with a grain of salt. A problem with 49,999 continuous variables and 1 binary is much easier to solve than a problem with 50,000 binaries.