Most current alignment software do both mapping and alignment together. In popular bioinformatics culture, alignment means mapping and alignment both. Purists will always refer to them differently (which is the correct way). The fundamental difference between mapping and alignment is that mapping is just knowing where the read comes from (it is an approximation). Alignment (which happens after mapping) is what defines how good the mapping is by applying various scoring schemes on matches and mismatches (different software have different scoring schemes). This is the overall concept. More information can be found at: Alignment and mapping

Alignment free tools can be found at: https://genomebiology.biomedcentral.com/articles/10.1186/s13059-019-1755-7