That is a good question. The definitions are quite similar.
GENDAI: nowadays (a-no), modern times, present-day.
SHINSAKU: new work, new production. It can also mean prosperity.
Broken down even further:
GEN: original (prefix)
DAI: title, subject, theme, topic
TO: sword
SHIN: new, genuineness.
SAKU: work or made (we know this to translate into "made this").
TO: sword
I too, as Rich Stein stated above, had always heard that the term Gendaito was used from the end of Shinshinto (1867) until post war production re-emerged in the early 1950's.
A couple of years ago I saw in Nagayama's book where the charts show "Gendaito" from 1867 thru Heisei 1989-.
The books definition states, SHINSAKUTO: Contemporary swords made by smith's who are still living.
I suppose Shinsakuto are technically Gendaito, but not vise versa. Shinsakuto are apparently designated as Gendaito when the smith dies.
Markus was right on track.
Ed M.