A LOT :)
Sevgi is more broad, you can have sevgi for your mother, siblings, animals etc. AŞK is only for the one you fell in love with. Of course you can also have SEVGİ for your partner, but aşk is stronger and more passionate
The same goes for the verbs sevmek and aşık olmak, you might say "seviyorum ama aşık değilim" - difficult to translate :)
aşık olmak > sevmek > hoşlanmak :)
another interesting note, sevgi is of Turkic origin and aşk is of Arabic origin. Sometimes loan words take a slightly different meaning; so I wonder if aşk is also a strong passionate love in Arabic or if it just means love :)
I'd like to point out a different aspect bu cümlede. Sevgi nedir = what love is. I've been wondering how to say something like that. A friend wrote on FB, "Mouse. It's what's for dinner," and ever since I've been wondering how that would be in Tk. "Fare: nedir akşam yemeği için." ??