The Securities and Exchange Commission is taking steps to eliminate some of the differences between the over-the-counter markets and the stock exchanges.

Last week, the commission authorized the country's stock exchanges to begin trading 25 over-the-counter stocks next Jan. 1. Previously, those stocks could be purchased only through brokers who are members of the National Association of Securities Dealers. This comes on the heels of an April decision in which the SEC gave permission for several exchanges to start trading in some options on over-the-counter stocks. (An option is the right, but not the obligation, to buy a certain stock at a given price by a specified date.)

Today the commission is scheduled to decide whether to allow the exchanges, along with the NASD, to begin a one-year pilot program in which six over-the-counter stocks and options on those stocks could be traded on a side-by-side basis. This would mark the first time that a dealer or firm would be allowed to trade both the stock and the option on that stock.

Side-by-side trading has not been permitted in the past for fear of price manipulation. The NASD, which opposes competition from the exchanges in the stocks it now trades exclusively, has appealed to the commission to reverse its April ruling.

Last week, the SEC voted to require broker dealers to disclose to customers the amount of markup or commission they make on over-the-counter transactions, starting next March 17. Commissions are supposed to be noted either in dollars or in fractions of a percentage point. The action, which brings the reporting of over-the-counter commissions in line with those of stocks listed on exchanges, presumably will make it easier for customers to do comparison shopping.

All the actions are designed to smooth out differences between markets with an eye to eventually creating a national market system, as Congress ordered in legislation passed a decade ago.

NORTHERN LINK . . . The commission will also be asked today to approve a link between the American Stock Exchange and the Toronto Stock Exchange. If approved, customers would be able to place orders at both exchanges for stocks traded across the border. The first such linkage was between the Boston and Montreal Stock Exchanges.

CANCELLATION . . . SEC Chairman John S.R. Shad, who was scheduled to address the National Press Club next Tuesday on major issues involving the securities markets, suddenly cancelled the longstanding engagement last week. Spokeswoman Mary McCue said the decision was made because of internal commission considerations. She declined to elaborate except to scotch rumors that Shad may be planning to resign. The speech will be rescheduled for a later date.

PERSONNEL CHANGES . . . Mary Joan Hoene has been named associate director of the SEC's Division of Investment Management. She replaces Jeffrey Steele, who has gone into private law practice in Washington. In addition, Carolyn B. Lewis has been appointed an assistant director in that division. A member of the SEC staff since 1962, Lewis will be responsible for the office that reviews and processes registration statements and other disclosure documents.

INSIDER OUTSIDE . . . Earlier this month, the SEC barred Adrian Antoniu from joining a brokerage firm dealing in over-the-counter stocks despite assurances from former associates and the NASD that he had been "rehabilitated." Antoniu pleaded guilty in 1980 to participating in a five-year scheme of insider trading, and received a suspended sentence of 39 months and a $5,000 fine.