The issue is that the indexes are compiled using different rules - especially about how they treat births to unmarried parents. That means that differences in results are inevitable (and can be quite useful sometimes).
For unmarried couples, where both parents are named, the "old" indexes, as seen on FreeBMD, index the child under both surnames. The "new" GRO index, in similar unmarried cases where both parents are named seems to only index under the father's name.
On FreeBMD, if you look at the other entries on the same page (1d 63) in St Saviour District, there are two other entries with the forenames Mary Ann.....under ALLEN and SAWKINS.
There are eleven entries on that page, but should only be ten, so one entry has been indexed twice.
There are scenarios in which your entry could be either of the above - but without obtaining the certificate it is impossible to be sure which.
You can still order a pdf, just use the normal ordering process and the reference you have from FreeBMD and select pdf copy as the delivery method.