I need some advice on using split sample regression versus regression with interaction term. My objective is to tell the [slope] difference, if any, between two groups [using a dummy].

Attached is a sample Stata output. The dependent variable is the Republican vote share in elections, the key independent variable is inflation, the dummy is 84 [coded 0 for before 1984, and 1 for 1984 and after], the controls are GDP and the Republican vote share in the last election. The interaction term is inflation*84.

My questions are:

1. How to interpret the different coefficients [slopes] results for Inflat? Specifically:
a. The coefficients are not the same between the Split sample regression [-0.0076 for 84=0; -0.0035 for 84=1] and the Regression with interaction term [-0.0075 for 84=0; -0.0037 for 84=1].
b. In the Split sample regression, the coefficient for Inflat is significant for 84=0 but insignificant for 84=1; but in the Regression with interaction term, the coefficient for the interaction term [hence the slope difference between 84=0 and 84=1] is insignificant [p-value=0.232].
2. How to relate and reconcile the slope analyses between the two approaches if I want to report both results?
3. When should I choose Split sample regression over Regression with interaction term, and vice versa?

I would be very grateful if the experts could give advice to my questions.

Thank you.