Partial String Lookup between two lists of Data

Hi there, I am trying to beef up a formula I have that we are using to search a list of existing companies for matches on a second often smaller list of companies. I will display the image below

But essentially I am trying to match up any company names that are similar, and need to be able to account for things like first list contains ABC Company limited. while the company I am trying to match to this is called ABC Company ltd.

My current formula to search these is

=MATCH("*"&C2&"*",A$2:A$6,0) I used ctrl+shift+enter

and the formula for the column that pulls the matched data is

=IF(ISNA(D2),"",INDEX(A$2:A$6,MATCH(C2,A$2:A$6,0)))

here is the way the data looks just as an example.

but basically I need to be able to search for most of a string, and to be able to ignore certain parts of the string to find a match. the pother way this comes into play is if a company is called Jones and Smith Inc. but they are on one list as Jones & Smith Inc.

in the below or attached picture I am matching up columns A and C

EXCEL Data sheet.JPG