Here's a quote of what Ian Hunter of bleacherreport.com say about the term "hometown discount" :That is a euphemism for the team that the player has been playing with and has formed bonds in the community, not born there.
"It's a term that's been thrown around quite often during this week's MLB hot stove —"hometown discount." For those unfamiliar with the term, a hometown discount is when a player takes a bit of a pay cut to play in the city that they grew up in, has family in, or is where they started their career."
In Shanahan's case, he was drafted by the Devils and that's where he started his career.