> select first 10 ifx_checksum(S.cat_descr,0),S.catalog_num , T.catalog_num, ifx_checksum(T.cat_descr,0) from catalog S, stores_demo@leap16_1_a_tcp:catalog T where S.catalog_num = T.catalog_num order by S.catalog_num ;

(expression) catalog_num catalog_num (expression) 

   286993076       10001       10001            0
   682015331       10002       10002            0
  1908503964       10003       10003            0
 -1025080793       10004       10004            0
  1125840401       10005       10005            0
  -377342203       10006       10006            0
 -1303427608       10007       10007            0
   538677152       10008       10008            0
  -214541734       10009       10009            0
 -2135660276       10010       10010            0

10 row(s) retrieved.

> select first 10 ifx_checksum(S.cat_descr,0),S.catalog_num , T.catalog_num, stores_demo@leap16_1_a_tcp:ifx_checksum(T.cat_descr,0) from catalog S, stores_demo@leap16_1_a_tcp:catalog T where S.catalog_num = T.catalog_num order by S.catalog_num ;

(expression) catalog_num catalog_num (expression) 

   286993076       10001       10001    286993076
   682015331       10002       10002    682015331
  1908503964       10003       10003   1908503964
 -1025080793       10004       10004  -1025080793
  1125840401       10005       10005   1125840401
  -377342203       10006       10006   -377342203
 -1303427608       10007       10007  -1303427608
   538677152       10008       10008    538677152
  -214541734       10009       10009   -214541734
 -2135660276       10010       10010  -2135660276

10 row(s) retrieved.

The difference is due to where is executed. In the first query, evaluated locally against a remote column from the database link, which results in values because the function is not properly pushed down/executed on the remote server. In the second query, explicitly forces the function to run on the remote server, so the correct checksum values are returned and they match the local table values.