What's the difference between conflict miss and capacity miss
The important distinction here is between cache misses caused by the size of your data set, and cache misses caused by the way your cache and data alignment are organized.
Lets assume you have a 32k direct mapped cache, and consider the following 2 cases:
You repeatedly iterate over a 128k array. There's no way the data can fit in that cache, therefore all the misses are capacity ones (except the first access of each line which is a compulsory miss, and would remain even if you could increase your cache infinitely).
You have 2 small 8k arrays, but unfortunately they are both aligned and map to the same sets. This means that while they could theoretically fit in the cache (if you fix your alignment), they will not utilize the full cache size and instead compete for the same group of sets and thrash each other. These are conflict misses, since the data could fit, but still collides due to organization. The same problem can occur with set associative caches, although less often (let's say the cache is 2-way, but you have 4 aligned data sets...).
The 2 types are indeed related, you could say that given high levels of associativity, set skewing, proper data alignments and other techniques, you could reduce the conflicts, until you're mostly left with true capacity misses that are unavoidable.
My favorite definition for conflict misses from Reducing Compulsory and Capacity misses by Norman P. Jouppi:
Conflict misses are misses that would not occur if the cache were fully associative with LRU replacement.
Let's look at an example. We have a direct-mapped cache of size of 4. The access sequences are
0(compulsory miss), 1(compulsory miss), 2(compulsory miss), 3(compulsory miss), 4(compulsory miss), 1(hit), 2(hit), 3(hit), 0(capacity miss), 4(capacity miss), 0(conflict miss)
The second to last 0 is a capacity miss because even if the cache were fully associative with LRU cache, it would still cause a miss because 4,1,2,3 are accessed before last 0. However the last 0 is a conflict miss because in a fully associative cache the last 4 would have replace 1 in the cache instead of 0.
Compulsory miss: when a block of main memory is trying to occupy fresh empty line of cache and the very first access to a memory Block that must be brought into cache is called compulsory miss.
Conflict miss: when still there are empty lines in the cache, block of main memory is conflicting with the already filled line of cache, ie., even when empty place is available, block is trying to occupy already filled line. its called conflict miss.
Capacity miss: miss occured when all lines of cache are filled.
conflict miss occurs only in direct mapped cache and set-associative cache. Because in associative mapping, no block of main memory tries to occupy already filled line.