Computer monitor versus television screen

I am using premiere elements 19 and have noticed that projects appear significantly brighter on my television screen than on my computer monitor.  Is this a recognised phenomenon?  I work on a project to get the picture right then save the project as an MP4 on a USB memory stick.  I then insert the memory stick into the television to see how it appears.  Both devices are high quality HD (Panasonic TV and Dell monitor) set on the factory default display pre-sets.  A commercially produced DVD also appears brighter on the TV than on the monitor.  As the intention is to produce DVDs to play on television sets I am assuming that I should make the picture to appear good on the TV and therefore to err on the dark side when working on the project on the computer.  However, it's a bit counter-intuitive!  Can you offer any advice?