Specs define these words in Division 01. Furnish usually means supply and deliver. Install usually means set in place and make ready. Provide usually means both.
Example: a spec says the equipment supplier furnishes floor sleeves and the flooring contractor installs them. The supplier prices the sleeves but no labor.
Read the verb on every item in your section. One word decides who pays for labor. In your proposal, state which items you furnish and install and which you furnish only. Check that another trade's section picks up the installation.