The first non-Numbers artifact I see is the "!" used in Excel to separate the worksheet name from the cell range in Excel.
The single quotes enclosing 'Chattanooga_State' are not needed in Numbers, nor is the underscore connecting the two words unless the underscore is used in the name itself.
In Numbers, the full address of a cell is Sheetname::Tablename::celladdress
If the cell (or range) in on the same table as the formula, only the celladdress is needed.
If the referenced cell is on a different table from the formula,
AND the name of the other table is distinct from the named on all other tables in the document,
Numbers needs Tablename::celladdress
If the referenced cell is on a different table than the formula
AND the name of that table is the same as any other tablename in the document,
Numbers needs the full Sheetname::Tablename::celladdress
Example:

The syntax for INDEX, MATCH and IFERROR is quite similar in Numbers and Excel
Numbers will provide you with that syntax in the Function Browser article for the specific function,
And will provide you with hints in the Formula Editor if you type the first few letters of the function name then choose the function from the suggestions provided.
Here's a Numbers formula written to do essentially the same lookup function as the Excel formula provided. All tables in the example are on the same sheet, but because each has a name distinct from all others in the document, the formula would not change if the two tables were on different sheets.

Register::A is a range reference to all of column A of that table (as shown by the highlighting in the cells in the table. Ditto for Register::D.
$A$1&" "&ROW()-1 constructs a text value (Baseball 1 in the selected cell) used as a search value by MATCH,
find value is the same instruction as 0 in the Excel version.
Regards,
Barry