I have done both. I would compare a sauna to a "sweat lodge" like a black and white photo to a 3d full color movie. Sweating is about all they have in common,

A sauna is a room that is heated hot enough to make you sweat. It can be a "dry" or a "steam" sauna. It tends to be passive (just sit and sweat) or conversation may be had with others in the room. Some may have a phone and other accessories.

On the other hand "sweat lodge" is a misleading simple label for the structure where a variety of ceremonies are performed. There is always a clear purpose that may encompass mental/emotional/spiritual elements as well as the physical. The lodge leader determines how best to serve the participants for a particular lodge ceremony. The hot stones brought in are not just stones but represent your ancestors who are with you to help you fulfill your reasons for participating in that lodge ceremony. This just scratches the surface of the topic. If you wish to know more, then of the lodge leaders I have sat with in the last 10 years I would contact Hawk Moon | Facebook

Finally a caution: Just like the quality of the answers to your question posted here, Lodge Leaders come in a variety of skill levels and types from Excellent, experienced, concerned for the people in their care -- to limited competency -- to inexperienced, ego driven (my opinion) people who have injured participants. Do your due diligence.

I have been participating in lodge ceremonies in both the USA and Canada for more than ten years with positive personal results that have kept me coming back for more.