They are the same in the meaning of "using", although "memakai" can be used in wider situations.
- "memakai" comes from the base verb "pakai".
- "menggunakan" comes from the base word "guna".
"memakai" can mean "wearing", "using", "obey/respect (rules), "require/spend", "ride" (transportation), "employ" (workers). While, "menggunakan" has three meanings: "using", "make use of" and "do something with".
For daily situations, we use both interchangeably in the context of "using".