Till – sediment derived from the erosion, transport, and deposition of glacier. Unsorted to poorly sorted in terms of grain size (includes clay, silt, sand, gravel, boulders, all sizes). Clasts are typically subangular to subrounded and usually include a diverse population of lithologies (rock types). Above are some photographs of modern/recent glacial environments (including the huge erratic left by the Laurentide Ice Sheet in New Hampshire). Notice the range in size and angularity.
Mudslide deposit – sediment transported by gravity and lubricated by water, sometimes triggered by earthquakes or storms, also result in an unsorted to poorly sorted deposit where clasts are subangular to subrounded. Lithology diversity would depend on the rock types available on the mountain slope.
Now imagine you are looking at an ancient rock, a conglomerate, that formed ~500,000,000 years ago and you are trying to decide if the rock is evidence of an ancient ice sheet or not. The conglomerate has rounded to subrounded clasts, a range in clast sizes, but all less than 50 cm in diameter, and just above the conglomerate is a layer with fine silts and clay laminations with some small gravel beds suggesting a lake or near-shore marine environment. The clasts look more rounded than the tills you have seen, the lithologies appear diverse, the largest clasts are smaller than what you have seen for till, and the conglomerate appears again above the laminated layer, suggesting a repeat event.
Geology is similar to forensics; you use the clues you have to infer what likely happened in the past. Finding a conglomerate that was once a till tells us about past climate and areas that must have had glaciers on them in the past.