DBCC SHRINKFILE WITH TRUNCATE_ONLY doesn't break the LSN (log sequence number) and cause you to lose your backup chain - all it does is remove the empty space from the file. If your tables have allocated space near the end of the file then you may not be able to release the space as you can only release file space down to the last active page in the file - but there may be free space in the file before this

BACKUP LOG WITH TRUNCATE_ONLY does break you LSN though, however this performs something completely different and won't claim space back - it will just flush the inactive portion of the log.

BACKUP LOG WITH TRUNCATE_ONLY has been deprecated and shouldn't be used - if your log files are growing set up a t-log backup job or set your databases to simple mode

a shrinkfile will not