lara, i have one of those too (solo card). here they just call them check cards. it was great cuz for the most part, i just use that instead of any of my other credit cards. usually, i'm buying stuff and i have money in the bank to back it up, so why use a credit card? it costs me since they throw in finance charges. so i use my check card instead.
now, when i wanted to get my chair from pier one, i used my pier one card because i didn't have enough money and wanted to pay it over time. i'm so happy, i managed to get a discover card (with a huge credit line! yay!), a sears mastercard, a pier one card, and an exxon gas card.
that's fucked up abel. me, i only don't get a statement if i DO pay it all in full. the only reason is because i make my credit card payments online and i told them to not send me statements because i don't need them. howevah, if i owe money (i usually try to pay before i get an invoice to avoid finance charges) then i get a statement. this is with discover, mind you. i don't remember what exxon does for me because i don't remember when was the last time i paid the bill (because i hardly drive anymore, i never need gas. my mom uses it and pays it for me instead, so it's almost more like her card, lol). i don't know about sears, i think they do the same thing discover does. i bought my mom a dishwasher for christmas and i paid it off like a week later, lol. pier one i think sends you stuff no matter what, but i dunno cuz i bought my chair in late november and i've not paid it off completely yet.