Most buyers when they refer to their ‘deposit’ mean the part of the purchase price that they are putting down themselves (i.e. usually the difference between the amount of the mortgage and the purchase price).
When Solicitors talk about the deposit they are referring to money that is handed over to the seller's Solicitors upon exchange of contracts.
On exchange of contracts the seller can insist on receiving from the buyer a 10% deposit of the purchase price. However, given that many people are not in a position to contribute as much as 10% to the purchase, reduced deposits are often agreed.
You should be aware, however, that if you are a buyer and you pay a reduced deposit then fail to complete the purchase through no fault of the seller, you will, under the terms of the contract, be required to make the deposit up to the full 10%.
You may also have to pay compensation to the seller if the seller loses out through your failure to complete.