Does League Manager do all the stuff that TM does plus match play events?

Tournament Manager is designed to run "Tournaments" such as gross, net, scrambles, best ball, points tournament, quotas, and many other types of tournament events.  Each format can be different for each tournament, and participates/pairings/teams are usually different for each tournament.
Tournament Manager lets you quickly signup who plays from a membership list, automatically generates pairings, etc...

League Manager is designed to run "leagues".  Leagues generally do not have the same concerns as those running tournaments.
For example, most "Team" leagues have set teams like in baseball and football and have a set schedule where each team or player plays against another team\player each week. They are not concerned about signing up different golfers each week and building different teams.  Their concern is usually a "Season" schedule, where each team plays against another team, rotation across different tees and courses, etc.  They also "usually" use substitutions for no shows, track stats throughout the season, track handicapping, etc.  Most leagues also translate who wins "what ever type of competition" they are playing into points to track season winners..but not all.  Some say best total net, total gross, etc, is the winner.  League Manager automatically tracks all this info.

Having said the above, both programs have the same features in many areas...I know some League Manager users use League Manager to run their mid and end of year tournaments...they create a "tournament" league, transfer golfers to this league and run tournament(s).  But if I was running many tournaments I would want to use the Tournament Manager...because it is specifically designed for this purpose...and is very fast for running tournaments.

A good analogy would be can use Microsoft Word to build spreadsheets in a document...but it's awkward.  If you were building many spreadsheets you would want to use Microsoft Excel because it's designed specifically for this purpose.