Ha! The cap and poster I have are from New Jersey Devils.
Rules do differ significantly. First and most important - in FIBA basketball there's no Defensive three-second violation. It allows defense (mostly centers) to occupy the paint for as long as they want and greatly reduces easy drives to the basket for a dunk or lay-up. It makes position of a center forward a lot more important.
Second difference is the length of the game. NBA plays 4x12 mins quarters. FIBA rules are 4x10 mins. Also FIBA basketball court is slightly smaller and 3-point line is a bit closer.
Players in NBA can call a timeout any time when in possession and so can coaches. In FIBA rules timeouts can only be called by coaches and only when the play has stopped.
As for timeouts, in NBA they are too long. The game drags because of it. In FIBA, timeout is strictly one minute. The FIBA game rarely exceeds 2 hours. In NBA a game goes for more than 2 hours and a half. So the pacing and importance of every play is higher in FIBA.
The travelling rules are also stricter in FIBA games. Player must dribble the ball before taking the first step. The current NBA tolerates a lot of travelling, especially if it results in splashy highlights. I think that a famous internet joke "NBA - Where Travelling happens" is true.
In FIBA, a player is permitted five personal fouls instead of six.
Also in FIBA basketball team work and defense is a lot more nuanced and significant. A lot of US players who come to play in Europe mention how surprised they are of the physicality of the game here. The current NBA trend of small ball and a lot of 3-pointers has taken away the beauty of the game. The last finals series and the quality of basketball I completely enjoyed was back in 2004 and 2005 when Pistons and Spurs won. I think Spurs is the best organization in modern NBA. But not many teams can replicate their style and success.
I think NBA creates a great basketball show that provides good entertainment and is financially viable. In Europe, I think, there isn't a single basketball team that recoups its expenses through income. European teams are either supported by big football clubs of the same name or sponsored by rich owners and through government and local provisions. So I think a basketball in Europe as it is today is a great luxury for fans because everyone is concentrated on the game instead of making money out of it.
Therefore I mostly just follow Euroleague and Spanish league games of Real Madrid. I'm glad that Luka Doncic is having a great career in NBA. As a young kid he was already a force to recon in Europe and a great leader in Madrid.
I used to watch a lot of CAVS games back when LeBron just started his career because another Lithuanian Zydrunas Ilgauskas (Big Z) played for most of his career in Clevaland and later had his jersey retired by the club. I'd like to see LeBron get another ring this season.