Does a three weeks monthly option chain has the same price compare to a three weeks weekly option chain?
Yes - but you may find that the weekly options dont have the same strike prices so hard to roll existing positions.
When the monthly option is 3 weeks away, it is identical to a weekly option chain that is 3 weeks away, except the monthly options will tend to have a higher open interest. FYI, they don't create both a weekly and monthly for the same date, so you never have both.
If they are the identical product: YES, else NO. (check the OPRA code if on TOS) References below specific to "S&P500 Index" When you say "monthly", it is not clear if you mean standard monthlies, and for what product. For example, monthlies for S&P500 Index can be AM settled, or PM settled. The PM settled (monthlies) are referenced via SPXPM, where the AM settled is referenced as SPX. Typically, if your referencing SPX products, the "Weekly" designation includes Monday, Wed, and Friday PM settled as well as the EOM PM settled products, which all have the prefix SPXW. The SPXPM products have the same settlement date as the SPX products, however, I know no one that trades the SPXPM, and it has lower liquidity.
With regard to your question, the date is all that is important unless the terms of the contract are different, such are american vs european and AM/PM expiration. If this is an equity option, just look at the date, the description of monthly vs weekly is no longer important.