Does FirstOrDefault return a reference to the item in the collection or the value?

var obj = myCollection.FirstOrDefault(x => x.Param == "match condition");  
if (obj != null)
{
    obj  = newObjectOfCollectionType; --> this will not reflect in the collection
}

var obj = myCollection.FirstOrDefault(x => x.Param == "match condition");  
if (obj != null)
{
    obj.Property = newValue; --> this will reflect in your object in the original collection
}

It does nothing to the collection. You can change the collection like this:

int index = myCollection.FindIndex(x => x.Param == "match condition");  
if (index != -1)
{
    myCollection[index]  = newObjectOfCollectionType;
}

it will do nothing; obj is a reference to the object (if the collection is of a reference type), and not the object itself.
If the collection is of a primitive type, then obj will be a copy of the value in the collection, and, again- this means that the collection will not change.

Edit:
to replace the object, it depends what your collection's type is.
If it's IEnumerable<T>, then it's not mutable, and you won't be able to change it.
The best option you have is to create a new collection and modify that, like so-

T [] array = myCollection.ToArray();
array[index] = newObject;