I want to sell my fine art photography online and also offer my training services for photographers (videos,books,workshops, etc). In trying to build a brand would it be best to have 2 separate sites or can I tastefully combine both as 1? In regards to SEO Does it matter if I have two different customer types & businesses on 1 site (people that buy pictures & people that want to make pictures)?
It does sound like you're targeting two different audiences because most photographers do not buy fine art photography from other photographers.
Because one offering (prints) is a product and the other (training) is a service, you'll have different messaging, and you'll need a different UI/UX to emphasize the value and benefits of each.
So though the thought of building a single, cohesive brand and directing ALL your traffic to one site might be appealing, going that route will probably introduce confusion.
I'd recommend one site for fine art photography. You can read a couple of dozen blog posts, and make a list of best practices for driving print sales.
And I'd recommend a second site for the training. Same thing here: go educate yourself on how to generate sales. Split test landing pages, focus on benefits, different calls to action, free "give them a taste" content, that sort of thing.
And then when it makes sense, you can always link the sites together using "My Other Projects" in the main nav, footer, or sidebar.
Would enjoy discussing more on a call if you're game.