The size of SMS messages is still fixed at 160 characters, but now they can be transparently chained to send longer texts. This is quite unlike IP protocols which have much larger maximum packet sizes.
Whether Twitter should ever have taken a cue from SMS is moot: apparently the Twitter creators were inspired by the way police and emergency services use radio, so terseness was an aesthetic choice.
The last time I tested it aaages ago, Twitter didn't enforce the encoding-based limitations, and if you sent a 140 character tweet full of unicode, it would actually send you several concatenated SMS.
It'd be interesting to see a Twitter clone where people could only communicate in https://en.wikipedia.org/wiki/Q_code (i.e. a code + its predefined strongly-typed parameters.)