Does the word "weisure" has the same meaning as leisure? If not, what is the difference?
Weisure is a portmanteau formed from work+leisure.It means working while in times of leisure.
Let me improve a bit the answers already offered.
It seems that the term was coined by Dalton Conley
As already stated by both @user69503 and @jsheeran, it's the merging of work and leisure. I've connected the dots when I though about the term in Spanish: trabajaciones
Here you can find interesting declarations by Conley himself but let me quote an excerpt
what it does mean is more and more Americans are using smartphones and other technology to collaborate with business colleagues while hanging out with their families
When I read the Spanish equivalent term trabajaciones (trabajo + vacaciones), I though that they were trying to sell us the idea that it's supercool to keep working on weekends and during holidays. I don't agree with them.
According to Wiktionary, it's a neologism with the definition:
The merging of work and leisure activities.
The only example it gives is from 2010, and the word doesn't appear to be in common use. I'd certainly never encountered it until reading it in your question.