Is there any practical difference between the following sentences?
a. That's the actual reason I'm going.
b. That's the reason I'm actually going.
I'd appreciate your help.
Yes, there certainly is a difference!
Using the actual reason implies there are other possible justifications for going - but in fact that is the real one.
Using I'm actually going implies that I could have responded in other possible ways - for example, I could have phoned or emailed, rather than going somewhere to meet with someone in person.
The long and short of it is that by default an adjective such as actual applies to the noun immediately following (emphasising that noun/thing is the real / relevant one, not something else). And by the same token, an adverb such as actually applies to the verb immediately following (emphasising that verb/action is the real / relevant one).