No - but they do share a kitchen.
Salad king is 'fast Thai food'. The emphasis is on turnover. And given the lineups they certainly satisfy the local cravings. Seating is communal.
Linda's is much more of a 'bistro'. Tablecloths, liveried servers and a more ambitious menu. You 'dine' rather than 'eat'. You can certainly order any item on the Salad King menu - but the treasures are in the 'special' items on the menu. Typically the dishes there take longer to prepare and are presented in a more upscale manner. I also find the spicing more complex -although both allow you to 'adjust the hotness' to your liking.
Typically we spand $20-30 (for two) at Salad King but maybe $75 at Linda's. Both are real deals.