Yes, the potential loss for a short seller of stock is almost unbounded but no stock has ever gone to infinity. Anyone with any experience with shorting would practice disciplined risk management should a short position move against him. Yes, a gap can hurt but no trader with a lick of sense doesn't cut losses.
As for long puts versus short stock, there are advantages and disadvantages for each:
Requires requires 50% margin overnight (US) but only 25% intraday for a Pattern Day Trader.
Stocks aren't always borrowable. If they are, the borrow cost may be next to nothing or it can be significant.
The delta of stock is 100 so without margin, it's a dollar for dollar gain or loss as the security moves. Margin leverage just multiplies the P&L in either direction.
The Alternative Uptick Rule is triggered when a stock experiences a price decline of at least 10% in one day. That may hinder your ability to open or add to a short position.
They must be paid for in full. The most that you can lose is the cost of the option.
They are a wasting asset so time decay (theta) erodes your position. Your window of opportunity is limited by expiration.
They can inflate in value if implied volatility expands and can lose value if it contracts (vega), regardless of share price.
Option B/A spreads tend to be wider than for equities, particularly for deep ITM options.
Pending dividends inflate the cost of a put and must be factored into option strategies calculations.
Liquidity? The options of some stocks trade by appointment (low Open Interest :-). Or it could be 10's of thousands of contracts a day in certain strikes if it's the widely traded SPY.
Options have a delta of zero to 100.
Deep ITM puts with a delta of 100 mimic the stock and P&L will be 1:1 to the downside but the loss ratio will decrease as the price of the security rises and the put's delta decreases.
ATM puts have a delta of about 50 so on a 1:1 basis, initially you'll make 50 cents on the dollar as the security drops.
OTM puts have a lower delta so they will appreciate fractionally but they offer greater leverage due to their low cost. Sort of like betting on the long shot horse at the track. If there is a volatility smile (skew), OTM puts be more expensive relative to closer to the money puts (not important if you get a big move in the underlying).
Which one is better involves one's experience, risk tolerance, time frame and discipline. In general, I'd say that shorting a security is more effective for short-term trades whereas a put may not respond much to intraday price movements (depends on the delta).
For longer time periods and for the less experienced and less disciplined, buy puts, despite all of its warts ;-)