"Regular coffee" depends on where you go and who you're talking to. For some people, it's made with instant coffee, white, or it could mean a drip coffee, or if at a cafe it might mean a flat white, latte or cappuccino in a regular sized cup. Or, a customer may have a certain coffee they like and tell the barista "I'll just have the regular, thanks".
Sorry i can't be more precise with that answer, but "regular coffee" is a very general term.
Cappuccinos, lattes and flat whites are both espresso based drinks (espresso being 30mL of strong, extracted coffee) topped up with steamed, textured milk.
A flat white is espresso plus milk with no froth, and is the weakest of the three. Served in a mug.
A latte is a espresso topped with silky steamed milk, with 1-2cm froth on top. Served in a glass.
A cappuccino should be 1/3 espresso, 1/3 milk and 1/3 froth but for most people that's too "dry" (meaning too much froth, not enough liquid) so usually is made with 2-3cm firm froth that has a dome shape. It's dusted with chocolate and served in a mug. A cappuccino is the strongest of the three, as it has less milk to dilute coffee.
If you want a stronger coffee, try a long black/americano (espresso topped with hot water), a short black (30mL shot of espresso), a ristretto (the first 10-15mL of an extraction), a macchiato (espresso topped with 15mL milk and a stain of froth) or add an extra shot or half shot to the drink.
Hope this answers your questions!
Barista, love coffee