To show you how meaningless the "interest" and offers are, I will give you my example...1985, my senior year...back then you got mailboxes full of introductory materials from schools who might be interested in you academically by checking a box allowing your ACT/SAT scores to be sent to schools "who might meet your educational level"...I must of gotten 200+ of the intro brochures from D3 or NAIA schools....If you filled out the postage prepaid card in the back of the brochure, they'd send you catalogs, more brochures, and send info to any programs you might be interested in...including athletics...
So I was a valedictorian of my class...30 ACT...I checked football and basketball as athletic interests...My high school didn't play football...I set school records for fewest points and rebounds in a season in basketball (zero for both) on a 2 win team as a junior...But I was 6'2", 220...I led the class in athletic visit offers (and I had 5 classmates who got girls volleyball scholarships, a teammate who got a hoops ride, and one who got a track/cc ride). I had schools specifically send admissions counselors to meet with me, bringing full athletic information questionaires...The valedictorian the year after me, who was an all-state basketball player with 1100+ career points and shooting 84% on free throws, got about the same number of visit offers...but nobody laughed about all his letters...lol
Moral of the story: getting a letter means someone told them you play a sport. Getting an offer means they actually think you could play there. Taking a visit means that you have put them in the top 5 or so of choices...Accepting a verbal offer means you are right now prepared to commit, but they don't have to accept and you can change your mind...and it keeps going...