If you are invited to a wedding and do not go, but you buy a nice
shower gift, do you also need to buy a wedding gift?

You never NEED to buy a gift. Gift-giving should never be compulsory.

Kriswrite

If you choose to attend, then , yes, you are pretty much obligated to
give (cash is always appreciated, despite what some might say).  If
you don't attend, then your relationship to the newlywed would dictate
whether you should give.

The proper thing to do for a friend or family member is to send a gift
within a year of the wedding, whether you attend or not.

Technically, the shower gift is for the bride, and the wedding gift is
for the couple.