Crossfit or lifting heavy

Yes and no.. lifting heavy requires picking things up and putting them down, crossfit adds speed and cardio in with that.
Crossfit relys on speed in a lot of their WOD's... this is generally considered dangerous for a beginner because they try to hurry and forget about form thereby injuring themselves. When done with an experienced crossfitter who focuses on good form over speed (but still pushes you obvs) it can be a great tool. Personally, I have seen too many injuries because of the nature and therefore recommend everyone have a good base/knowledge of form prior to starting with crossfit to help reduce the chance of injury. (logic says they'll adhere to form even it it takes a few seconds off their time... prob doesnt apply to everyone). So my suggestion is lift heavy first until you get the form correct and are confident with it.
Edit: Side note... I suck at explaining things so sorry if this doesn't flow well...
ETA: Experience: EMT on military base.

Is crossfit the same as lifting heavy? What is the diffrence between them? I am a beginer which one should I start.

Not supposed to be, lifting heavy, you go really heavy. I was a power lifter and that heavy is not the same as crossfit.

I have done both, right now I am cross fitting because the box is right near my house and I find it to be an efficient workout--I leave 2 minutes before class and home 2 minutes after and I get it all done at once in an hour vs driving to the 'big' gym, parking, etc.

I also found that when I was primarily lifting and doing cardio, I either had to be at the gym for 1.5 hours, or go a lot to get both in--and as a working mom time is my priority. that being said, I think for body recomposition and weight loss, heavy lifting plus cardio is going to get you results faster.

In terms of the differences between the two:

Crossfit--as least as it is trained where I go-- incorporates a lot of cardio and HIIT, and my biggest improvement since starting is quad strength, upper body strength and cardiovascular conditioning. But it does not focus on the major muscle areas in a consistent way--like legs, abs, back, etc that you could do when you design your own lifting, and I'm a little less 'sculpted' than when I did a lot of lifting. However, I'm in better cardio shape because of the intensity of the work outs versus when I did cardio on my own and never really pushed it (you know, the elliptical watching a TV show for 25 minutes type of cardio....).

Instead of focusing on a couple body areas, cross fit varies between different types of lifts, speed work, endurance work, plyometrics, gymnastics, etc. So you become a little better at a lot of things, rather than very good/strong at a few--and if you do it long enough and consistently enough, you will get very good at a lot of things. This is good for people who can either go all the time, or get bored easily, or don't have the specific goal of building lots of muscle mass (I think heavy lifting is better for that). Its also good for people who are more motivated by class structure and other people--I know I am more likely to go to a 6 am cross fit class than to get my butt to the gym and lift on my own, but everyone's different.
.

In cross fit, there's a warm up, then usually one or two skills to practice--anything from a specific lift (snatch, overhead squats) to a skill like jump roping, pull ups, or handstands--sometimes its strength based, sometimes is speed or cardio or another skill.

Then there's the "workout of the day" which is a short (sometimes 8 minutes, sometimes 20-25) intense work out that usually mixes a couple elements but generally is intensive both cardio and strength wise--although I ALWAYS use a lower weight during the WOD than during any lifting portion because I am careful about injuries.
If you do cross fit, make sure to take a basic training course first so that you have good form. If the instructor pushes specific weights, or does not tell you how to scale things if you need to, go elsewhere. and if you're the type who is really competitive and does stupid stuff to impress other people, you will get injured.

hope this helps.