Honestly you can wear them both as sport jackets and they'll be fine. Technically though - the former (solid light grey wool or cotton/wool blend) and the latter (presumably navy birdseye) are both business suit fabrics/patterns.
A traditional sport jacket usually possesses four features - casual fabrics such as cotton, seersucker, linen or tweed, casual patterns such as windowpane, notch lapels, horn buttons (metal being more of a blazer thing and buttons matching fabric being more of a suit thing) and the optional patch pockets. (your grey jacket has flap pockets and the navy has besom)
So if we're really counting, these are strictly orphaned suit jackets and should not be used as sport jackets - but then again in the streets we now walk on nobody gives a crap, it's just not the most flattering choice to wear without matching pants. But then again I often wear my wide peak lapeled suit jackets with other dress pants so I'm not the one to talk.
I don't mind the skinny lapels if you've the build for it - which no one should have when it's at 2.36 but that's your preference.
ps this is a pretty safe look for a sports jacket
I cannot thank you enough for your help!! :)