While I understand theta (time decay) in options, I often see theta being computed for linear products as well (outright FX forwards). What is theta in this case then? And how is it different from the interest rate sensitivity that comes from the forward points?
I think your FX theta is probably not the same as the theta in black scholes sense.
I think it may mean time pnl, which is applicable to all products, i.e., the PnL of time passing 1 day, but keeping all the market data the same. Note that here you have two markets, market 1 (original market) and market 2 (the original market's but moving 1 day forward)
For options, one part of time pnl would come from theta. For linear products, a part would come from the 1 day less of accrual.