What is the difference between ten minute walk and ten minutes' walk, are they the same?
The meaning is practically the same but the grammar is not.
You can use this in a couple of ways:
ten minutes' walk
ten minutes of walk
walk of ten minutes
Notice the hyphens in the first two cases. Words like those are called compound adjectives. It's like saying "short walk" but you specify it as "ten-minute" or "ten-minute-long".
The other three are possessive, and even though the possessor and the possessed switch places in case four and five, they still mean the same thing: a walk that lasted for ten minutes.
It should be noted that you use the last form also when you talk about some experience, something with importance, e.g.
a walk of the year
a run of the century
a journey of a lifetime
but in these cases the meaning does differ, the time is not the duration, it's usually a time frame in which something happened. It's like saying "the best walk this year", "the best run of this century" and "the best journey of your life".
They mean the same, but for different reasons.
For the apostrophe version, note that you should use minute's only for one minute, and minutes' for more than one minute. Note that the apostrophe has moved in the plural. For an explanation, check out this link.
When you add the apostrophe, you make a genitive, so it means the same as ten minutes of walking: the ten minutes is a measure of a quantity of walking, ie a distance.
Without the apostrophe, it's like a compound noun, with ten minute describing walk: that's why minute is singular. You are talking about a walk with a duration of ten minutes. Ten minutes is simply a measure of time.
According to this Ngram, the genitive form used to be the only one: The non-apostrophe form came into existence around 1910, and became the most widely used in 1980.
This switch in usage is probably a result of changes in society's attitude to walking. It is no longer the normal means of getting about, but a form of exercise. You have to exercise for ten minutes, rather than to get from A to B.