I have the Explorer Club Visa Card - the one that costs $395 a year that's mean to include membership to the Red Carpet Club (now United Club). What they were telling me was that the Explorer Club Credit Card and Explorer Credit Card (one says Club, one does not, right?) are exactly the same.
I think the confusion everyone as seeing was the combining of two different card names into one. There is the "Mileage Plus Explorer Card" and the "Mileage Plus Club Card". There is no "Mileage Plus Explorer Club Card". (Note: There are a few more cards out there but they're not able to be applied for, namely The Presidential Plus card and the Awards card which replaced legacy UA and CO cards).
https://www.chase.com/online/Credit-Cards/united.htm
What you need to do before flying again is the following: Go to a United Club, ask them to print you a temporary card, it will look like a boarding pass. When Club card stopped working I had them do this, I didn't have any problems at the US lounges in DCA or PHL after this.
You will also want to call the UAC number to speak to someone and make sure your membership has been fully processed. It takes them long enough to just post miles, one can only imagine how long it takes to get a membership done. 1-866-UA-CLUBS (1-866-822-5827) 8 a.m. to 8 p.m. (CT), daily. You're not getting the benefit of your bargain, so you do need to take some initiative to make that call.
For the record, it shouldn't take much more than 1-2 weeks to get the card on the top end. My replacement cards have been showing up usually at the start of the month that the old card expires.