Under normal circumstances:

STBY means standby and you should not expect not to get aboard, but you can have hope.
GTE means gate assigned, and you should expect to be aboard... somewhere. Maybe stuck in the back, maybe lazyUpd or at least priority seated by a busy agent. Could go either way.

Under irregular circumstances, STBY probably means you are entirely boned, and GTE means you are priority to be boned next. Unless you have super high status and are indirectly responsible for someone else getting boned and kicked off GTE, STBY or confirmed seating.