There are some more specific variations between landscape architects and landscape designers depending on state, but this is (I think) a pretty decent summary: http://www.revolutionarygardens.com/do-i-need-a-landscape-designer-or-a-landscape-architect/

Anyhow, to your other point: a wise mentor once told me that the #1 goal of the landscape design process is to remove uncertainty from the equation. Making it awesome and gorgeous and so incredibly cool that your friends and neighbors will seethe with jealousy? Totally part of it too, BUT our job is to make sure that you know what you're getting, how it will look, how it will function, how it will cost, and in your case - how it could be phased in over time.

So why would you pay someone when other guys will give it away for free? You may be comparing apples and bicycles. Here's why. My design process includes meeting with the client to figure out not just what they want but what their tastes are, what's their personal style, and - this is the most important part and what I love - what is the story you have in your head about how your family will live in the new space I'm creating for you?

Then it's a significant amount of time doing the site analysis, taking all that data to create a base plan, then working through concepts until I come up with something that works, then fleshing that out and getting the details right. From there it's also whatever else is part of the presentation (for me that may include photos of recommended plant materials and hardscape finishes, section or elevation drawings, and budgeting breakouts). I don't live a lavish lifestyle but I spoil my dog, so I need to get paid for that significant outlay of time. I'm not saying that the contractor giving out free designs isn't doing an ok job, but for a $100k project you probably want an awesome job.

As to your worries about whether or not you'll like the finished design, well... that's a question you need to ask your designer. Here are some ways I soothe my clients' nerves if they have that worry: http://www.revolutionarygardens.com/what-if-i-dont-like-the-design-you-create-dave/

But it's important to point out that you need to not only pick a designer who has a portfolio you like but one who you "click" with. This person needs to get inside your head and not just know how to make the design work for the site but work for you. And that comes back to your concern about the design blowing the budget out of the water. If the designer is applying the fees to the build it sounds like he wants to build it. So that means 1) blowing you out of the water with an unreasonable budget (assuming you've shared your target budget with him) is a stupid idea on his end and 2) he's now given you a document that facilitates apples-to-apples comparisons. That doesn't mean he needs to do it cheaper than anyone else, but he should be able to justify why his price is higher for the same portion.

We're talking about committing 1.2% of your stated budget to be certain of the outcome of the project. I think as long as you have confidence in the designer it's money well spent.