Can I buy into a business the same way I'd buy shares, if it's actually a partnership?

Not quite — a partnership isn't a corporation, so there are no shares to buy in the legal sense. Instead, "buying in" generally means being admitted as a partner and acquiring a partnership interest, governed by the partnership agreement between the existing partners, or by general partnership law principles if there's no written agreement at all. The mechanics, and the risks, are genuinely different from a share purchase.

The nuance that matters most is liability. In a general partnership, partners can be personally liable for the partnership's debts and obligations, not just to the extent of what they invested, which is a materially different risk profile than owning shares in a corporation. Depending on how the partnership is structured, and whether it's a limited partnership with both general and limited partners, your personal exposure as an incoming partner can vary significantly, and that needs to be understood before you commit anything.

It's also worth knowing that a partnership interest generally doesn't qualify for the tax treatment available to an individual selling qualifying small business corporation shares, since that specifically requires shares of a corporation. A business lawyer should review the existing partnership agreement and your actual exposure before you buy in.