Mortgage and pledge are often used and freely interchanged, when used in common parlance. However, they have very big differences.
1) Movable and immovable assets
You always say, "I pledged my shares", you never say that "I mortgaged my shares". So, pledge is used for movable assets like shares, securities, fixed deposits etc. On the other hand, you would never say, "I pledged by apartment".
So, in short, mortgage is a term that is used for fixed assets like land, buildings, apartments etc.
When you pledge your shares, they would still remain with you and you would be entitled to dividends etc. However, when you mortgage your apartment, the documents would remain with the lender. It could either be banks or any other lending institution. Though in this case you would be free to rent your apartment.
3) Easy to sell a pledged asset rather than a mortgaged one
It's easier to sell a pledged asset by the lender, if the borrower fails to pay the amount. However, in certain cases there could be a legal binding in the case of a mortgaged property and intervention of the Court maybe necessary.
Now let us explain the difference between pledge and hypthothecation with an example:
You can pledge a whole lot of things in India, including gold and financial instruments like shares and post office saving schemes or even your life insurance policy. In this case, the bank or the concerned institution will receive the documents or gold as the case maybe. If there is a default on the principal and interest after requisite notices, than the bank or the financial institution has the right to sell the financial instruments or gold as the case maybe.
They will than proceed to recover the money from such a pledged asset.
One of the best examples, to give of a mortgaged asset would be an apartment that is with a home loan. The concerned bank would keep the documents, though the owner has the full right to rent the property. However, he cannot sell the property unless the bank's dues are paid. This is not possible as the bank would retain the original sale deed and other important documents.
There are other important terms that also one needs to study along with mortgage and pledge. These include assignment and hypothecation. Example of Hypothecation would be a two-wheeler loan, which you have taken from a bank. The vehicles would be co-owned by the bank and the client. Once the loan is paid, the bank would give a letter and the owner can get the vehicle transferred only on his name.