It depends on the firm's model. The title "partner" is not always used to mean a "partner" in the strict legal sense.
Equity partners are generally "proper" partners in that they, in partnership, own the firm. As such, they can only get money by selling or diluting their equity or through dividends (creaming off excess profits).
In a large partnership firm, there may be some stability around the dividend, or the partners may agree to some stabilising mechanism so that they can still take dividends in loss years without detracting excessively from investment in the firm. They may refer to this dividend income as a "salary" for convenience. However, their earnings (and losses, if it isn't a limited liability partnership) are potentially as volatile as any other self-employed businessperson.
Salaried partners are a bit of a contradiction in terms, but clearly there's a cachet attached to being called a "partner" which helps with staff retention. In publicly-owned firms, such as Accenture, they sometimes avoid the issue by calling the most senior people "senior executives" or such since nobody is a "partner" in the full legal sense. As with any public company, senior management often choose to buy stock, may be required to hold stock as a director, or may have stock options. They are equity-holders without being equity partners.
Conventionally, all partners are equal. However, in many larger firms where there are hundreds of partners, such an decision-making structure would make for chaos. Therefore, there are multiple levels of partners (regular partner vs. managing partner for example) - this may be part of the formal governance structure, based on size of investment (in smaller firms), or may be informal (e.g. founding partners get special treatment).
Because of the big legal difference in status, salaried partners and equity partners don't tend to coexist with the same job title. If you take a loose view of "partner" then, yes, there are firms where salaried partner is the step before equity partner. However, there are also cases where the salaried partner role is used to get in a senior seller who doesn't want to commit to full partnership or who the firm doesn't expect to need long-term.
In smaller firms, without a large equity base, partners need to buy their equity or invest a certain amount to become a partner. This is a tied investment for as long as they are a partner. In larger firms, which have plenty of equity, it would be horrendously expensive to buy a reasonable sized partnership. Therefore, the convention is for partners to take a loan from the firm to buy their equity. They pay a peppercorn interest rate on the loan so the financial commitment and risk is much smaller than it would normally be.