More often than not transactions do effect Asset and Liabilities. For your example of a Cheque and savings account, while these have a sub designation of bank accounts they are both Assets so a transfer between them reduces the value of one and increases the value of the other, so it changes the value of these assets. A credit card is a type of liability account.
Say you have an investment property and you set up an account for it under the Asset heading, If its purchase is reflect as a transfer from a bank account you see the bank account value decrease ( this asset is worth less) and the value of the house account increased (the value of this asset has gone up)
What do you mean by changes in stock position? If you are talking about changes in value caused by the movement on the market this is reflect in the share price and reports in Moneydance can use the current share price to show the value. If you are talking about changes in holdings then you use buy and sell transactions to do this.
The bottom line is at the highest level there are only 4 "types" of accounts; Assets, Liabilities, Income & Expense any other type is a sub type of these.
I am a Quicken user and I am considering changing.
Your email was very helpful.
What I meant by changes in stock position is the following. Suppose you
have a retirement account with equities in it. The person managing it
decides to sell 100 shares of General Motors and replace it with shares
of Tesla. When the shares of General Motors get sold, there is cash
generated, perhaps a gain on the sale, and a reinvestment of the cash to
the Tesla stock. Can the investment account handle this?