They can express different ideas of what "together with" means. See Substructural Logics
For example, in many logics, there is a structural rule that says you can go from $A;B\vdash C$ to $B;A\vdash C$ (often call the rule of Exchange). Another rule says you can go from $A;A\vdash B$ to $A\vdash B$ (rule of Contraction). Etc. They're called structural rather than logical rules because they set the meaning of (non-logical) punctuation marks like ";" in these examples. Real-world analogs: suppose A and B represent events in the first example, and $A;B$ means "event A, then event B", and the rule of Exchange does not hold. Note that we could add a second mark $A,B$ to express that both events occurred in either order.
In the second example, suppose A means "one dollar" and B means "cup of coffee", so $A;A\vdash B$ means that two dollars will get you a cup of coffee, and the rule of Contraction does not hold. So in this case the informal notion of a resource that can be consumed can be expressed as a purely formal Structural Rule.
By defining different punctuation marks and selecting various structural rules you get lots of different ways of interpreting "A together with B"; logics that can be used to model lots of different things.