They are the same. Some cities have their own leagues, it is called Baja, here. Little League, Pony, etc. is called rec here. It is OK to say Little League, especially if you are asking about rules.
rec league is a generic term for a recreation league as opposed to tournament level or "travel" ball.
rec teams are the community teams where whoever signs up plays, travel teams are the ones that hold tryouts and normally have girls from several different communities.
Little League is national governing organization, which has both baseball and softball under its umbrella. ASA is another national governing organization. There are others.
Upper Midwest states like ours are a little different. In MN, the term Rec League is where cities create small leagues within their Park and Rec programs. Travel Ball is any team that “travels” outside of their city for games. Our “State” tournaments are almost all local teams and each year we crown about a dozen “champions” at each age level. Our “National“ tournaments draw from as far away as WI and SD!
Thankfully we do have a few true club programs that have had some national success recently and hopefully that trend will continue.