Q:

partial google sheets string cell comparison

The Primary Sheet has basic info ( narrowed here ), including 
Column B - a flag to say "Yes" or "No/Stop"
Column C  - a Company Name
A Second sheet "stopphrases" will have a growing list of words and phrases in it. If one of these words match first sheet called "data" > Column C (Company Name), Column B will updated to a "No"
IE - 
1) If stopphrases!sheet, range A1:A25 contains "UPS"
2) And the Primary Sheet has "UPS Shipping"
This "partial" match should catch it and insert flag into data.Column B
=MATCH(""&stopphrases!A1:A10&"", C6,0)
I seem to be able to check a partial from a single cell and check the range, but not got the other way - get the partial words from multiple cells and check against a single cell. 
I also tried
(If Statement)
=IF(COUNTA(IFERROR(FILTER(stopphrases!$A$1:$A$25,stopphrases!$A$1:$A$25=C2))),"Yes","No")
The results I am looking for are
So again - 
IF StopPhrases!A1:A25 Range has a phrase "UPS"
THen any entry in first sheet, Company Name, Column B that CONTAINS "UPS" - IE "UPS Shipping" should flag - this way I can run a condition.
The end result is if a match occurs a "stop" happens and that record doesn't get processed in other spreadsheets that are connected.

A:

You can use regexmatch or regexextract to do this: 
first to make the dynamic list of stopphrases you use a JOIN function, an INDIRECT function so you  can use COUNTA to allow for it to automatically add the correct number of phrases, 
 =JOIN("|",INDIRECT("E2:E"&COUNTA(E2:E)+1))

Then you use arrayformula and regexmatch to dynamically match your list of stop words:
=ARRAYFORMULA(IF(ISTEXT(B1:B),if(REGEXMATCH(B1:B,$D$1),"STOP","GO"),))

=ARRAYFORMULA(IF(ISTEXT(B1:B),if(REGEXMATCH(LOWER(B1:B),$D$1),"STOP","GO"),))

