Specific compounds in reactions don't matter as much as the mechanism which they bring to the reaction, with the exception of whatever it is you are reacting.
Chemistry is not about memorizing and learning what chemicals make certain reactions happen, but learning about how those chemicals behave in solution and how they can interact with other compounds, and from this, we can gain a deeper understanding of why reactions do what they do.
For your example, HCl, H2SO4, H3O+, H+ , are all used to represent protons in solution, or in other words, acidic solutions. With of course, HCl, and H2SO4 giving specific examples. At first glance you might infer that acids can easily be interchanged, which they can, depending on the reaction conditions, but this is definitely not the case in most reactions. This is why it is important to gain an understanding of the electron and proton transfers behind various reactions so that you can make conclusions about what compounds you can interchange, and which you cannot. With Na and Li metals being exchanged, this is probably because they are both fairly powerful deprotonating agents.
This is why I love chemistry. It's almost like magic. When you understand the mechanisms, the possibilities that open up to you are endless. Very rarely is there ever one specific way to do a reaction, nor is there ever one specific way to synthesize a certain compound. There are millions of ways, many of which have been undiscovered for whatever reason. For instance, new Catalysts get created every day that behave in a ways never before seen, that can open thousands of doors for so many reactions.
I don't think your professor will expect more from you than what they expect/teach. If you are ever in doubt, just ask them. It is good to differentiate between these little details to gain a deeper understanding, because you will be so far ahead of everyone else in the class.