When Carmy kisses Claire, in contrast to calmer songs like "this is what love is for" with Sydney, the music sings "I can hardly wait, I can't wait" also supporting the motif of clocks constantly appearing around Claire as a sort of count down (where there are none or they are even turned off around Sydney), the other shoe dropping, and the feeling of urgency with Claire.
It's what he always wanted and others want for him and he likes her so he has to get her now he can't wait, not out of desire but out of fear. The other shoe could drop any second so he can't risk waiting until tomorrow for anything.
While with Sydney, the clocks shut off and it calms to just straining broth together. He has to kiss Claire right now because who knows what'll happen - and that's romantic in other contexts. But not when "I have to now" is written in contrast to "you slow down time".
He views Claire with a - I didn't even think about it when I first typed this but - "Sense of Urgency". He doesn't need more urgency in his life.
Claire is "Sense Of Urgency".
Sydney is "Every Second Counts"
- In the way it was meant to be interpreted as described in Forks: appreciate the little things and allow yourself to slow down. Every second counts, so cherish them, don't rush by and lose them.
Edit: we don't hate on competing love interests or pit women against each other here please stfu in the comments.