As /r/bodangren2 notes, differentiation can mean content, process, environments, or products.
I differentiate like crazy and you know where I used differentiation the most? Where I spent most of my career: At an inner city Title 1 middle school that I left due to its "failing school" status (I had gains and great student scores, but the school of a whole tanked the last few years of tests). Differentiation vastly improves behavioral management within the classroom, in my experience. I'd actually consider it a classroom management tool because kids who feel supported (lower) or properly extended (higher) are much less likely to engage in disruption.
I used to write up contracts for various independent grading metrics, based on improvement, whilst still showing them their score based on the standardized testing rubric and criteria. I used to record texts on tape myself or get copies of recordings so students would have an audio option, utilizing technology. I used to pull texts at various lexiles for lexile-based reading groups. I used to pull small groups for re-teaches regularly. I used centers and had students rotate through the centers they needed (I'd make 8 or so and students would do 4 each or whatever, based on need). Lots of ways to differentiate, especially when you don't lean too hard on Whole Group Instruction.
I still do these things, but honestly, much less, just because my students are much more homogeneous and successful at my new suburban middle school. I only have 5 students who are low enough to be graded on alternate grading contracts this year. I only have 3 classes where there's ever a group low enough to pull for a small group for the whole class period and I utilize small group check-ins instead.
I'm not sure what your specialists have suggested "differentiation" means or entails or what solutions they've given, but it absolutely can and should be done. Granted, I think all students should see a lot of the same content, assignments, etc, if in the same exact course (ADVANCED being different from REGULAR is fine, but the course should -- with all teachers of the grade -- be defined by the same standards, etc) but that doesn't mean no differentiation happens.