Recently, I had a conversation at a conference with an educator, who claimed universal design for learning is learning styles, so we should use learning styles in instruction or training.
No, they are not the same.
Universal design for learning (UDL) facilitates the achievement of learning goals for individuals with learning differences and capabilities , as it provides a blueprint and framework to create instructional goals, content, and assessment that can suit everyone .
UDL consists of three main blocks tailored to the instructional environment  that addresses learning differences . These are multiple means of:
1) Presentation: using a variety of ways to present the content to help learners acquire knowledge , e.g. text to speech 
2) Action and expression: encouraging learners to demonstrate their learning in a variety of ways, such as writing an essay, recording an audio response or creating a video 
3) Engagement: using a range of practices and adjustable levels of challenge to enhance learners’ motivation , e.g. TheReadingbar software that contains a volume control slider 
Considering learning differences and the pace of learning in different individuals, implementing UDL could help learners who cannot keep up with their peers, or have some learning disabilities. UDL does not just provide accessibility, but it eliminates barriers so every learner can succeed . Organizations and instructional designers could use UDL in their learning design process. Extensive research has proven that the use of UDL supports strategic learning and enhance learners’ learning experience [3, 7, 8].
As you see, UDL is different than learning styles, which has been debunked due to not having any supporting evidence. In contrast, research on UDL has been widely replicated and grounded in learning sciences, neuroscience, and cognitive science. It is deeply rooted in Zone of Proximal Development (ZPD), scaffolding, and modeling.
If you are interested, learn more about UDL here.
(1) Trostle Brand, S., Favazza, A., & Dalton, E. (2012). Universal design for learning: A blueprint for success for all learners. Kappa Delta Pi Record, 48(3), 134-139.
(2) Tobin, T.J. (2014). Increase online student retention with universal design for learning. Quarterly Review of Distance Education, 15(3), p13-24. 12 pp.
(3) Schelly, C.L, Davies, P.L. & Spooner, C.L. (2011). Student perceptions of faculty implementation of universal design for learning. Journal of Postsecondary Education and Disability, 24(1), 17-30. Retrieved from https://files.eric.ed.gov/fulltext/EJ941729.pdf
(4) CAST (2011). Universal design for learning guidelines.Retrieved from www.udlcenter.org
(5) Edyburn, D.L. (2005). Universal design for learning. Retrieved from http://www.ocali.org/up_doc/UDL_SETP7.pdf
(6) Novak, K. (2016). UDL now!: A teacher’s guide to applying universal design for learning in today’s classrooms. CAST Professional Publishing, 45, 237-238.
(7) Smith, F.G. (2012). Analyzing a Ccollege course that adheres to the universal design for learning (UDL) framework. Journal of the Scholarship of Teaching and Learning, 12(3), 31 – 61. Retrieved from https://files.eric.ed.gov/fulltext/EJ992116.pdf
(8) Spencer, J. &Whittaker, C.R. (2017). UDL A Blueprint for Learning Success. Educational Leadership, 74(7), 59-63.