"Dressy casual" is almost a contradiction in terms. When I was a human resources director (I've been retired several years), my company approved "business casual" attire for workers.
Business casualwear is more comfortable than the more formal businesswear of old. Think pressed khaki slacks with a navy blazer and low-heeled (but closed toe) shoes rather than a dressy suit and high heels.
You can find many examples (with photos) of business casualwear via search engines or books. The key, I think, is that if it's too casual, it's not for work. You're not taken seriously at work if you don't dress neatly and with a measure of thoughtfulness about what you're wearing. This is especially important for a woman.
Your daughter's boss may be using the word "dressy" with casual to get across the point that dressing in a manner that is too casual is not appropriate for work, but to save for after work. Employees who show up for work looking sloppy may be sent home to change clothing! However, if your daughter isn't sure what the term means in her company, she should ask her new boss for guidelines about what is acceptable and what is not acceptable.
Your daughter can dress appropriately for her job in business casual attire without breaking the budget. Try discount stores or even thrift shops to find good-looking clothing that will fit the description for inexpensive cost.