Subject to buyer selling their home:
If you are a buyer that already owns a house or condo and your offer is made, "Subject to selling your current home," then you are referred to as a "contingent buyer" because you need to sell your current home in order to buy the next one. 

This may be one potentially weak point for you when trying to buy another home.  The reason is that the seller of that property may be concerned that the need for you to sell your current home first may interfere with the sale of their property to you.  However, if your current home already has an accepted offer then this may make your offer to the seller stronger. 

If you do already have an accepted offer for your property, then there are some other items that the seller will want to know about before they accept your offer.  These items include, whether or not the buyers for your current home have already had their home inspection, whether or not your buyers have a mortgage commitment (not just a "Prequalification Letter"), and have your buyers signed a P&S agreement with you and given a good sized deposit? 

Again, the seller of the property will want to know if the above items have been completed and if they have not been done, then they will want to know when they are going to be completed.  When you are making your offer to the seller you should include this information with a cover letter explaining the current status of the property you are selling.  This will help the sellers make an informed decision.  It may also help you get your offer accepted because the seller will be less apprehensive about the status of your property.

 
Subject to seller finding suitable housing:
You may find a house or condo that is, "Subject to seller finding suitable housing."  This means that the sellers will only sell you their property if they can find another one to buy.  Sometimes the sellers are given a certain amount of time to accomplish this and sometimes it is open-ended.   Seller sometimes add this disclosure if they are nervous about finding the next place they want to buy. 

The risk for you, as the buyer in this type of transaction, is that the sellers may not find something else to buy and therefore, they would not be obligated to sell you the property.  This is true even if you have signed a Purchase and Sales agreement, have given a deposit on the property and/or if you have spent money on a home inspection.  If the sellers do not find another place, then they do not have to sell you the property, thus they are supposed to return your deposit money.

Again, you may want to consult with an attorney if you are entering into an agreement that is, "Subject to seller finding suitable housing."